Sample records for solutal convection vermiculated

Full Text Available This paper summarizes the basis for the solution of heat removal by natural convection from both conventional nuclear reactors and reactors with fuel flowing coolant (such as reactors with molten fluoride salts MSR.The possibility of intensification of heat removal through gas lift is focused on. It might be used in an MSR (Molten Salt Reactor for cleaning the salt mixture of degassed fission products and therefore eliminating problems with iodine pitting. Heat removal by natural convection and its intensification increases significantly the safety of nuclear reactors. Simultaneously the heat removal also solves problems with lifetime of pumps in the primary circuit of high-temperature reactors.

Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically. (paper)

Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically.

We describe experiments in which crystals of NaCl, KBr, and KCl are dissolved from below by aqueous solutions containing concentrations of the respective salts from zero concentration to near saturation. The solution near the solid-liquid interface is gravitationally unstable, producing turbulent hydrodynamic motion similar to thermal convection from a single surface cooled from above. The coupling of the fluid flow with the solid dissolution produces irregular patterns at the solid-liquid interface with a distribution of horizontal length scales. The dissolution mass flux and the pattern length scales are compared with a turbulent boundary layer model. Remarkable agreement is found, showing that the fluid motion controls both the dissolution rate and the interface patterning. copyright 1996 The American Physical Society

Full Text Available In this paper, numerical solutions for convection-diffusion equation via non-polynomial splines are studied. We purpose an implicit method based on non-polynomial spline functions for solving the convection-diffusion equation. The method is proven to be unconditionally stable by using Von Neumann technique. Numerical results are illustrated to demonstrate the efficiency and stability of the purposed method.

Full Text Available A numerical technique based on the Hermite interpolant multiscaling functions is presented for the solution of Convection-diusion equations. The operational matrices of derivative, integration and product are presented for multiscaling functions and are utilized to reduce the solution of linear Convection-diusion equation to the solution of algebraic equations. Because of sparsity of these matrices, this method is computationally very attractive and reduces the CPU time and computer memory. Illustrative examples are included to demonstrate the validity and applicability of the new technique.

This paper presents a class of backward free-convective boundary-layer similarity solutions. It is shown that these boundary layers can be produced along slender downward-projecting slabs of prescribed thickness variation, which are infinitely long. It is pointed out that these solutions can be used

Rock fractures invaded by a water flow, are often subjected to dissolution, which let grow and evolve the initial fracture network, by evacuating the eroded minerals under a solute form. In the case of fast kinetic of dissolution, local erosion rate is set by the advection of the solute. The erosion velocity decreases indeed with the solute concentration at the interface and vanishes when this concentration reaches the saturation value. Even in absence of an imposed or external flow, advection can drive the dissolution, when buoyancy effects due to gravity induce a solutalconvection flow, which controls the erosive dynamics and modifies the shape of the dissolving interface. Here, we investigate using model experiments with fast dissolving materials and numerical simulations in simplified situations, solutalconvection induced by dissolution. Results are interpreted regarding a linear stability analysis of the corresponding solutal Rayleigh-Benard instability. A dissolving surface is suspended above a water height, initially at rest. In a first step, solute flux is transported through a growing diffusion layer. Then after an onset time, once the layer exceeds critical width, convection flow starts under the form of falling plumes. A dynamic equilibrium results in average from births and deaths of intermittent plumes, setting the size of the solute concentration boundary layer at the interface and thus the erosion velocity. Solutalconvection can also induce a pattern on the dissolving interface. We show experimentally with suspended and inclined blocks of salt and sugar, that in a linear stage, the first wavelength of the dissolution pattern corresponds to the wavelength of the convection instability. Then pattern evolves to more complex shapes due to non-linear interactions between the flow and the eroded interface. More generally, we inquire what are the conditions to observe a such solutalconvection instability in geological situations and if the properties of

Despite its popularity in many engineering fields, the nonlinear diffusion-convection equation has no general analytical solutions. This work presents a family of closed-form analytical traveling wave solutions for the nonlinear diffusion-convection equation with power law nonlinearities. This kind of equations typically appears in nonlinear problems of flow and transport in porous media. The solutions that are addressed are simple and fully analytical. Three classes of analytical solutions are presented depending on the type of the nonlinear diffusion coefficient (increasing, decreasing or constant). It has shown that the structure of the traveling wave solution is strongly related to the diffusion term. The main advantage of the proposed solutions is that they are presented in a unified form contrary to existing solutions in the literature where the derivation of each solution depends on the specific values of the diffusion and convection parameters. The proposed closed-form solutions are simple to use, do not require any numerical implementation, and may be implemented in a simple spreadsheet. The analytical expressions are also useful to mathematically analyze the structure and properties of the solutions.

Numerical solutions of three-dimensional compressible hydrodynamics (including sound waves) in a stratified medium with open boundaries are presented. Convergent/divergent points play a controlling role in the flows, which are dominated by a single frequency related to the mean sound crossing time. Superposed on these rapid compressive flows, slower eddy-like flows eventually create convective transport. The solutions contain small structures stacked on top of larger ones, with vertical scales equal to the local pressure scale heights, H sub p. Although convective transport starts later in the evolution, vertical scales of H sub p are apparently selected at much earlier times by nonlinear compressive effects.

Studies to examine the effect of solutalconvection on crystal morphology using sucrose as a model system were initiated. Aspect ratios, defined as the width of the 100-plane-oriented face over the width of the 001-plane-oriented face, were determined for oriented crystals which were grown with either the 001-oriented or the 100-oriented face perpendicular to the convective flow. The dependence of the crystal morphology on orientation is much greater for crystals grown with one face occluded than for crystals grown suspended in solution. Many factors appear to interact in a complex fashion to influence crystal morphology.

In this article, an analytical solution for a Marangoni mixed convection boundary layer flow is presented. A similarity transform reduces the Navier-Stokes equations to a set of nonlinear ordinary differential equations, which are solved analytically by means of the homotopy analysis method (HAM...... the convergence of the solution. The numerical solution of the similarity equations is developed and the results are in good agreement with the analytical results based on the HAM....

In recent years numerical solutions of the convective heat transfer equations have provided significant insight into the complex materials processing operations. However, these computational methods suffer from two major shortcomings. First, these procedures are designed to calculate temperature fields and cooling rates as output and the unidirectional structure of these solutions preclude specification of these variables as input even when their desired values are known. Second, and more important, these procedures cannot determine multiple pathways or multiple sets of input variables to achieve a particular output from the convective heat transfer equations. Here we propose a new method that overcomes the aforementioned shortcomings of the commonly used solutions of the convective heat transfer equations. The procedure combines the conventional numerical solution methods with a real number based genetic algorithm (GA) to achieve bi-directionality, i.e. the ability to calculate the required input variables to achieve a specific output such as temperature field or cooling rate. More important, the ability of the GA to find a population of solutions enables this procedure to search for and find multiple sets of input variables, all of which can lead to the desired specific output. The proposed computational procedure has been applied to convective heat transfer in a liquid layer locally heated on its free surface by an electric arc, where various sets of input variables are computed to achieve a specific fusion zone geometry defined by an equilibrium temperature. Good agreement is achieved between the model predictions and the independent experimental results, indicating significant promise for the application of this procedure in finding multiple solutions of convective heat transfer equations

Based on the prognostic equations of mixed-layer theory assuming a zeroth order jump at the entrainment zone, analytical solutions for the boundary-layer height evolution are derived with different degrees of accuracy. First, an exact implicit expression for the boundary-layer height for a situation

In this paper, we employ a new approximate analytical method called the optimal homotopy asymptotic method (OHAM) to solve steady state heat transfer problem in slabs. The heat transfer problem is modeled using nonlinear two-point boundary value problem. Using OHAM, we obtained the approximate analytical solution for dimensionless temperature with different values of a parameter ε. Further, the OHAM results for dimensionless temperature have been presented graphically and in tabular form. Comparison has been provided with existing results from the use of homotopy perturbation method, perturbation method and numerical method. For numerical results, we used Runge-Kutta Fehlberg fourth-fifth order method. It was found that OHAM produces better approximate analytical solutions than those which are obtained by homotopy perturbation and perturbation methods, in the sense of closer agreement with results obtained from the use of Runge-Kutta Fehlberg fourth-fifth order method.

A stabilizing-correction scheme is constructed for integrating the fourth-order equation describing the dynamics of a viscous incompressible liquid. As an example, a solution is obtained to the problem of the solidification of a liquid in a rectangular region with allowance for convective energy transfer in the liquid phase as well as temperature-dependent changes of viscosity. It is noted that the proposed method can be used to study steady-state problems of thermal convection in ingots obtained through continuous casting.

Previous experimental and analytical studies of solute transport in the intervertebral disc have demonstrated that for small molecules diffusive transport alone fulfils the nutritional needs of disc cells. It has been often suggested that fluid flow into and within the disc may enhance the transport of larger molecules. The goal of the study was to predict the influence of load-induced interstitial fluid flow on mass transport in the intervertebral disc. An iterative procedure was used to predict the convective transport of physiologically relevant molecules within the disc. An axisymmetric, poroelastic finite-element structural model of the disc was developed. The diurnal loading was divided into discrete time steps. At each time step, the fluid flow within the disc due to compression or swelling was calculated. A sequentially coupled diffusion/convection model was then employed to calculate solute transport, with a constant concentration of solute being provided at the vascularised endplates and outer annulus. Loading was simulated for a complete diurnal cycle, and the relative convective and diffusive transport was compared for solutes with molecular weights ranging from 400 Da to 40 kDa. Consistent with previous studies, fluid flow did not enhance the transport of low-weight solutes. During swelling, interstitial fluid flow increased the unidirectional penetration of large solutes by approximately 100%. Due to the bi-directional temporal nature of disc loading, however, the net effect of convective transport over a full diurnal cycle was more limited (30% increase). Further study is required to determine the significance of large solutes and the timing of their delivery for disc physiology.

A numerical simulation study was carried out to investigate the relative contributions of thermal and solutal Marangoni convections on transport structures in a liquid bridge under zero gravity. The liquid bridge in the model represents a three dimensional half-zone configuration of the Floating Zone (FZ) growth system. Three dimensional field equations of the liquid zone, i.e. continuity, momentum, energy, and diffusion equations, were solved by the PISO algorithm. Computations were performed using the open source software OpenFOAM. The numerical simulation results show that the flow field becomes three-dimensional and time-depended when the solutal Marangoni number is larger than the critical value. It was also shown that not only flow patterns but also the azimuthal wave number (m) changes due to the competing contributions of thermal and solutal Marangoni convective flows.

Double diffusive natural convection within a vertical porous enclosure with localized heating and salting from one side is numerically studied by the finite element based finite volume method. In the formulation of the problem, use is made of the Darcy model, which allows the slip boundary condition on a solid wall to be satisfied. Comparisons with benchmark solutions for natural convection in fluid saturated porous enclosures are first presented to validate the code. Following that, an extensive series of numerical simulations is conducted in the range of -55 {<=} N {<=} + 55 and 0.125 {<=} L {<=} 0.875, where N and L are the buoyancy ratio and the element location, respectively. Streamlines, heatlines, masslines, isotherms and iso-concentrations in the system are produced to illustrate the flow structure transition from solutal dominated opposing to thermal dominated and solutal dominated aiding flows, respectively. The computed average Nusselt and Sherwood numbers provide guidance for locating the heating and salting element. (author)

Double diffusive natural convection within a vertical porous enclosure with localized heating and salting from one side is numerically studied by the finite element based finite volume method. In the formulation of the problem, use is made of the Darcy model, which allows the slip boundary condition on a solid wall to be satisfied. Comparisons with benchmark solutions for natural convection in fluid saturated porous enclosures are first presented to validate the code. Following that, an extensive series of numerical simulations is conducted in the range of -55 {<=} N {<=} + 55 and 0.125 {<=} L {<=} 0.875, where N and L are the buoyancy ratio and the element location, respectively. Streamlines, heatlines, masslines, isotherms and iso-concentrations in the system are produced to illustrate the flow structure transition from solutal dominated opposing to thermal dominated and solutal dominated aiding flows, respectively. The computed average Nusselt and Sherwood numbers provide guidance for locating the heating and salting element.

Transitions and bifurcations of transient natural convection in a horizontal annulus with radiatively participating medium are numerically investigated using the coupled lattice Boltzmann and direct collocation meshless (LB-DCM) method. As a hybrid approach based on a common multi-scale Boltzmann-type model, the LB-DCM scheme is easy to implement and has an excellent flexibility in dealing with the irregular geometries. Separate particle distribution functions in the LBM are used to calculate the density field, the velocity field and the thermal field. In the radiatively participating medium, the contribution of thermal radiation to natural convection must be taken into account, and it is considered as a radiative term in the energy equation that is solved by the meshless method with moving least-squares (MLS) approximation. The occurrence of various instabilities and bifurcative phenomena is analyzed for different Rayleigh number Ra and Prandtl number Pr with and without radiation. Then, bifurcation diagrams and dual solutions are presented for relevant radiative parameters, such as convection-radiation parameter Rc and optical thickness τ. Numerical results show that the presence of volumetric radiation changes the static temperature gradient of the fluid, and generally results in an increase in the flow critical value. Besides, the existence and development of dual solutions of transient convection in the presence of radiation are greatly affected by radiative parameters. Finally, the advantage of LB-DCM combination is discussed, and the potential benefits of applying the LB-DCM method to multi-field coupling problems are demonstrated.

The transport of a spherical solute through a long circular cylindrical pore filled with an electrolyte solution is studied numerically, in the presence of constant surface charge on the solute and the pore wall. Fluid dynamic analyses were carried out to calculate the flow field around the solute in the pore to evaluate the drag coefficients exerted on the solute. Electrical potentials around the solute in the electrolyte solution were computed based on a mean-field theory to provide the interaction energy between the charged solute and the pore wall. Combining the results of the fluid dynamic and electrostatic analyses, we estimated the rate of the diffusive and convective transport of the solute across the pore. Although the present estimates of the drag coefficients on the solute suggest more than 10% difference from existing studies, depending on the radius ratio of the solute relative to the pore and the radial position of the solute center in the pore, this difference leads to a minor effect on the hindrance factors. It was found that even at rather large ion concentrations, the repulsive electrostatic interaction between the charged solute and the pore wall of like charge could significantly reduce the transport rate of the solute.

Full Text Available The generalized integral transform technique (GITT is employed to obtain a hybrid numerical-analytical solution of natural convection in a cavity with volumetric heat generation. The hybrid nature of this approach allows for the establishment of benchmark results in the solution of non-linear partial differential equation systems, including the coupled set of heat and fluid flow equations that govern the steady natural convection problem under consideration. Through performing the GITT, the resulting transformed ODE system is then numerically solved by making use of the subroutine DBVPFD from the IMSL Library. Therefore, numerical results under user prescribed accuracy are obtained for different values of Rayleigh numbers, and the convergence behavior of the proposed eigenfunction expansions is illustrated. Critical comparisons against solutions produced by ANSYS CFX 12.0 are then conducted, which demonstrate excellent agreement. Several sets of reference results for natural convection with volumetric heat generation in a bi-dimensional square cavity are also provided for future verification of numerical results obtained by other researchers.

Full Text Available This paper presents an analytical model of substrate mass transfer through the lumen of a membrane bioreactor. The model is a solution of the convective-diffusion equation in two dimensions using a regular perturbation technique. The analysis accounts for radial-convective flow as well as axial diffusion of the substrate specie. The model is applicable to the different modes of operation of membrane bioreactor (MBR systems (e.g., dead-end, open-shell, or closed-shell mode, as well as the vertical or horizontal orientation. The first-order limit of the Michaelis-Menten equation for substrate consumption was used to test the developed model against available analytical results. The results obtained from the application of this model, along with a biofilm growth kinetic model, will be useful in the derivation of an efficiency expression for enzyme production in an MBR.

Full Text Available This article investigates the unsteady free convection flow of a micropolar fluid over a vertical plate oscillating in its own plane with Newtonian heating condition. The problem is modelled in terms of partial differential equations with some physical conditions. Closed form solutions in terms of exponential and complementary error functions of Gauss are obtained by using the Laplace transform technique. They satisfy the governing equations and impose boundary and initial conditions. The present solution in the absence of microrotation reduces to well-known solutions of Newtonian fluid. Graphs are plotted to study the effects of various physical parameters on velocity and microrotation. Numerical results for skin friction and wall couple stress is computed in tables. Apart from the engineering point of view, the present article has strong advantage over the published literature as the exact solutions obtained here can be used as a benchmark for comparison with numerical/ approximate solutions and experimental data.

A novel concept of double optimal linearization is introduced and used to obtain a simple and accurate solution for the temperature distribution in a straight rectangular convective-radiative fin with temperature dependent thermal conductivity. The solution is built from the classical solution for a pure convection fin of constant thermal conductivity which appears in terms of hyperbolic functions. When compared with the direct numerical solution, the double optimally linearized solution is found to be accurate within 4% for a range of radiation-conduction and thermal conductivity parameters that are likely to be encountered in practice. The present solution is simple and offers superior accuracy compared with the fairly complex approximate solutions based on the homotopy perturbation method, variational iteration method, and the double series regular perturbation method. The fin efficiency expression resembles the classical result for the constant thermal conductivity convecting fin. The present results are easily usable by the practicing engineers in their thermal design and analysis work involving fins.

The theory and use of the finite element code TRIP are described. The code calculates temperature distributions in three-dimensional continua subjected to convection heat transfer. A variational principle for transport phenomena is applied to solve the convection heat transfer problem with temperature and heat flux boundary conditions. The finite element discretization technique is used to reduce the continuous spatial solution into a finite number of unknowns. The method is developed in detail to determine temperature distributions in coolant passages of fuel rod bundles which are idealized by hexahedral elements. The development of the TRIP code is discussed and the listing of the program is given in FORTRAN IV. An example is given to illustrate the validity and practicality of the method

Peeling of tomatoes by radiative heating is a valid alternative to steam or lye, which are expensive and pollutant methods. Suitable energy densities are required in order to realize short time operations, thus involving only a thin layer under the tomato surface. This paper aims to predict the temperature field in rotating tomatoes exposed to the source irradiation. Therefore, a 1D unsteady analytical model is presented, which involves a semi-infinite slab subjected to time dependent heating while convective heat transfer takes place on the exposed surface. In order to account for the tomato rotation, the heat source is described as the positive half-wave of a sinusoidal function. The problem being linear, the solution is derived following the Laplace Transform Method. In addition, an easy-to-handle solution for the problem at hand is presented, which assumes a differentiable function for approximating the source while neglecting convective cooling, the latter contribution turning out to be negligible for the context at hand. A satisfying agreement between the two analytical solutions is found, therefore, an easy procedure for a proper design of the dry heating system can be set up avoiding the use of numerical simulations.

The aim of this paper is to present an explicit numerical algorithm based on improved spectral Galerkin method for solving the unsteady diffusion-convection-reaction equation. The principal characteristics of this approach give the explicit eigenvalues and eigenvectors based on the time-space separation method and boundary condition analysis. With the help of Fourier series and Galerkin truncation, we can obtain the finite-dimensional ordinary differential equations which facilitate the system analysis and controller design. By comparing with the finite element method, the numerical solutions are demonstrated via two examples. It is shown that the proposed method is effective.

Full Text Available The approximate analytical solution of a problem about nonstationary free convection in the conductive and laminar mode of the Newtonian liquid in square area at the instantaneous change of temperature of a sidewall and lack of heat fluxes is submitted on top and bottom the bases. The equations of free convection in an approximation of Oberbeka-Bussinesk are linearized due to neglect by convective items. For reduction of number of hydrothermal parameters the system is given to the dimensionless look by introduction of scales for effect and explanatory variables. Transition from classical variables to the variables "whirlwind-a flow function" allowed to reduce system to a nonstationary heat conduction equation and a nonstationary nonuniform biharmonic equation, and the first is not dependent on the second. The decision in the form of a flow function is received by application integral a sine - Fourier transforms with terminating limits to a biharmonic equation at first on a variable x, and then on a variable y. The flow function has an appearance of a double series of Fourier on sine with coefficients in an integral form. Coefficients of a row represent integrals from unknown functions. On the basis of a hypothesis of an express type of integrals coefficients are calculated from the linear equation system received from boundary conditions on partial derivatives of function. Dependence of structure of a current on Prandtl's number is investigated. The cards of streamlines and isolines of components of speed describing development of a current from the moment of emergence before transition to a stationary state are received. The schedules of a field of vectors of speeds in various time illustrating dynamics of a current are provided. Reliability of a hypothesis of an express type of integral coefficients is confirmed by adequacy to physical sense and coherence of the received results with the numerical solution of a problem.

A numerical simulation study was carried out to investigate the effect of thermo-solutal Marangoni convection on the flow patterns and the azimuthal wave number (m) in a liquid bridge under zero-gravity. The liquid bridge in the model represents a three dimensional half-zone configuration of the Floating Zone (FZ) growth system. Three dimensional field equations of the liquid zone, i.e. continuity, momentum, energy, and diffusion equations, were solved by the PISO algorithm. The physical properties of the silicon-germanium melt were used (Pr=6.37×10-3 and Sc=14.0, where Pr and Sc stand for the Prandtl number and the Schmidt number). The aspect ratio Asp was set to 0.5 (Asp= L/a, where L and a stand for the length of free surface and the radius of liquid bridge). Computations were performed using the open source software OpenFOAM. The numerical simulation results show that the co-existence of thermal and solutal Marangoni convections significantly affects the azimuthal wave number m in the liquid bridge.

In this research work a numerical model for the solution of two-dimensional natural convection problems in arbitrary cavities of a Boussinesq fluid is presented. The conservation equations are written in a general curvilinear coordinate system which matches the irregular boundaries of the domain. The nonorthogonal system is generated by a suitable system of elliptic equations. The momentum and continuity equations are transformed from the Cartesian system to the general curvilinear system keeping the Cartesian velocity components as the dependent variables in the transformed domain. Finite difference equations are obtained for the contravariant velocity components in the transformed domain. The numerical calculations are performed in a fixed rectangular domain and both the Cartesian and the contravariant velocity components take part in the solutiomn procedure. The dependent variables are arranged on the grid in a staggered manner. The numerical model is tested by solving the driven flow in a square cavity with a moving side using a nonorthogoanl grid. The natural convenction in a square cavity, using an orthogonal and a nonorthogonal grid, is also solved for the model test. Also, the solution for the buoyancy flow between a square cylinder placed inside a circular cylinder is presented. The results of the test problems are compared with those available in the specialized literature. Finally, in order to show the generality of the model, the natural convection problem inside a very irregular cavity is presented. (Author) [pt

Pyrite is one of the most common accessory minerals in many rocks and generally occurs in hydrothermal deposit. However, pyrite morphology and association with other sulfide minerals is not well known with respect to the solution condition, especially with the hydrothermal solution under circulation. In this study, recrystallization experiments of pyrite from circulating hydrothermal solution by thermal convection were carried out. A rectangular circuit (42.6 cm by 17.3 cm) of SUS316 pressure tubing with 5 mm in inner diameter was used as a reaction vessel. The volume of the circuit is approximately 24 ml. Long sides of the rectangular circuit were held to be 20 degrees inclination. One of the long sides was heated by an electric furnace. Solution in the circuit evaporates in the high temperature tubing and the vapor condenses in room temperature tubing. The solution backs to the bottom of the high temperature tubing. Thus, thermal convection of the solution produces circulation in the circuit. Starting material was filled in the high temperature tubing. The lower half was filled with mixture of 2 g of powdered natural pyrite and 4 g of quartz grains. The upper half was filled with quartz grains only. 9 ml of 5 mol/l NH4Cl solution was sealed in the circuit with the starting material. Temperature gradient of the sample was monitored by 6 thermocouples. Maximum temperature was controlled at 350°C. Experimental durations are 3, 5, 10 and 30 days. After the experiments, the run products are fixed with resin and cut every 2 cm. Thin sections of vertical cross-sections are made and observed by microscope and SEM. Tiny pyrite crystals occurred at the upper outside of the furnace, where temperature should be much lower than 200°C. In the lower half of the starting material, pyrite decomposed and pyrrhotite formed around pyrite grains. At higher temperature area, pyrite decomposition and pyrrhotite formation is remarkable. Circulating sulfur-bearing solution provided by

This article focuses on the flow of Maxwell nanofluids with graphene nanoparticles over a vertical plate (static) with constant wall temperature. Possessing high thermal conductivity, engine oil is useful to be chosen as base fluid with free convection. The problem is modelled in terms of PDE’s with boundary conditions. Some suitable non-dimensional variables are interposed to transform the governing equations into dimensionless form. The generated equations are solved via Laplace transform technique. Exact solutions are evaluated for velocity and temperature. These solutions are significantly controlled by some parameters involved. Temperature rises with elevation in volume fraction while Velocity decreases with increment in volume fraction. A comparison with previous published results are established and discussed. Moreover, a detailed discussion is made for influence of volume fraction on the flow and heat profile.

The disposal of high-level radioactive wastes in deep geological formations is of pronounced technological importance for nuclear safety. The understanding of related fluid flow, heat and mass transport in geological systems is of great interest. This article prepares necessary physical, mathematical and numerical fundamentals for computational modeling of related phenomena. The porous media is described by the simple Darcy law and momentum-energy coupling is due to Boussinesq approximation. The Dual Reciprocity of Boundary Element Method (DRBEM) is used for solving coupled mass, momentum and energy equations in two-dimensions for the steady buoyancy induced convection problem in an semi-infinite porous media. It is structured by weighting with the fundamental solution of the Laplace equation. The inverse multi quadrics are used in the DRBEM transformation. The solution is obtained in an iterative way.(author)

Most of the recent studies of CO2 sequestration are performed in open systems where the constant partial pressure of CO2 in the vapor phase results in a time-invariant saturated concentration of CO2 in the brine (Cs). However, in some closed natural CO2 reservoirs, e.g., Bravo Dome in New Mexico, the continuous dissolution of CO2 leads to a pressure drop in the gas that is accompanied by a reduction of Cs and thereby affects the dynamics and mass transport of convection in the brine. In this talk, I discuss the characteristics of convective CO2 dissolution in a closed system. The gas is assumed to be ideal and its solubility given by Henry's law. An analytical solution shows that the diffusive base state is no longer self-similar and that diffusive mass transfer declines rapidly. Scaling analysis reveals that the volume ratio of brine and gas η determines the behavior of the system. DNS show that no constant flux regime exists for η > 0 nevertheless, the quantity F /Cs2 remains constant, where F is the dissolution flux. The onset time is only affected by η when the Rayleigh number Ra is small. In this case, the drop in Cs during the initial diffusive regime significantly reduces the effective Ra and therefore delays the onset.

The vast majority of numerical investigations of transport phenomena use an Eulerian formulation for the convenience that the computational grids are fixed in space. An Eulerian-Lagrangian method (ELM) of solution for the convection-dispersion equation is discussed and analyzed. The ELM uses the Lagrangian concept in an Eulerian computational grid system. The values of the dependent variable off the grid are calculated by interpolation. When a linear interpolation is used, the method is a slight improvement over the upwind difference method. At this level of approximation both the ELM and the upwind difference method suffer from large numerical dispersion. However, if second-order Lagrangian polynomials are used in the interpolation, the ELM is proven to be free of artificial numerical dispersion for the convection-dispersion equation. The concept of the ELM is extended for treatment of anisotropic dispersion in natural coordinates. In this approach the anisotropic properties of dispersion can be conveniently related to the properties of the flow field. Several numerical examples are given to further substantiate the results of the present analysis.

This paper presents an examination of numerical results for the buoyancy-driven convection heat transfer problem, in a two-dimensional enclosure under steady-state, laminar, incompressible, and temperature dependent viscosity fluid flow conditions. The vertical walls are exposed to different temperatures and the top and bottom are insulated. Rayleigh numbers of 10{sup 4}, 10{sup 5}, and 10{sup 6} are considered. Specific heat, thermal conductivity, and the thermal expansion coefficient are assumed constant. Density variation is included using the Oberbeck-Boussinesq approximation. The results are obtained using the SIMPLEC solution technique based on a power-law, finite-volume discretization scheme. The hydrodynamic and thermal fields are presented at various locations in the enclosures.

A “glymphatic system,” which involves convective fluid transport from para-arterial to paravenous cerebrospinal fluid through brain extracellular space (ECS), has been proposed to account for solute clearance in brain, and aquaporin-4 water channels in astrocyte endfeet may have a role in this process. Here, we investigate the major predictions of the glymphatic mechanism by modeling diffusive and convective transport in brain ECS and by solving the Navier–Stokes and convection–diffusion equations, using realistic ECS geometry for short-range transport between para-arterial and paravenous spaces. Major model parameters include para-arterial and paravenous pressures, ECS volume fraction, solute diffusion coefficient, and astrocyte foot-process water permeability. The model predicts solute accumulation and clearance from the ECS after a step change in solute concentration in para-arterial fluid. The principal and robust conclusions of the model are as follows: (a) significant convective transport requires a sustained pressure difference of several mmHg between the para-arterial and paravenous fluid and is not affected by pulsatile pressure fluctuations; (b) astrocyte endfoot water permeability does not substantially alter the rate of convective transport in ECS as the resistance to flow across endfeet is far greater than in the gaps surrounding them; and (c) diffusion (without convection) in the ECS is adequate to account for experimental transport studies in brain parenchyma. Therefore, our modeling results do not support a physiologically important role for local parenchymal convective flow in solute transport through brain ECS. PMID:27836940

Full Text Available In this paper, we have achieved high order solution of a three dimensional nonlinear diffusive-convective problem using modified variational iteration method. The efficiency of this approach has been shown by solving two examples. All computational work has been performed in MATHEMATICA.

Full Text Available In this paper, the $(G'/G$-expansion method is applied to solve a biological reaction-convection-diffusion model arising in mathematical biology. Exact traveling wave solutions are obtained by this method. This scheme can be applied to a wide class of nonlinear partial differential equations.

In this paper, we propose the concept of the perturbed invariant subspaces (PISs), and study the approximate generalized functional variable separation solution for the nonlinear diffusion-convection equation with weak source by the approximate generalized conditional symmetries (AGCSs) related to the PISs. Complete classification of the perturbed equations which admit the approximate generalized functional separable solutions (AGFSSs) is obtained. As a consequence, some AGFSSs to the resulting equations are explicitly constructed by way of examples.

Full Text Available This paper investigates the double stratified effects in mixed convection three-dimensional flow of an Oldroyd-B nanofluid. The flow is due to a bidirectional stretching surface. Mathematical analysis is carried out using the temperature and concentration stratification effects. Brownian motion, thermophoresis and chemical reaction effects are also considered. The governing nonlinear boundary layer equations are first converted into the dimensionless ordinary differential equations and then solved for the convergent series solutions of velocity, temperature and nanoparticles concentration. Convergence analysis of the obtained series solutions is also checked and verified. Effects of various emerging parameters are studied in details. Numerical values of local Nusselt and Sherwood numbers are tabulated and analyzed. It is noticed that the impact of mixed convection parameter on temperature and nanoparticles concentration is quite similar. Both temperature and nanoparticles concentration are reduced for larger mixed convection parameter. Keywords: Three-dimensional flow, Oldroyd-B fluid, Nanoparticles, Mixed convection, Thermal and solutal stratification, Chemically reactive species

The three-pore model of peritoneal membrane physiology predicts sieving of small solutes as a result of the presence of a water-exclusive pathway. The purpose of this study was to measure the diffusive and convective components of small solute transport, including water, under differing convection. Triplicate studies were performed in eight stable individuals using 2-L exchanges of bicarbonate buffered 1.36 or 3.86% glucose and icodextrin. Diffusion of water was estimated by establishing an artificial gradient of deuterated water (HDO) between blood/body water and the dialysate. (125)RISA (radio-iodinated serum albumin) was used as an intraperitoneal volume marker to determine the net ultrafiltration and reabsorption of fluid. The mass transfer area coefficient (MTAC) for HDO and solutes was estimated using the Garred and Waniewski equations. The MTAC of HDO calculated for 1.36% glucose and icodextrin were similar (36.8 versus 39.7 ml/min; P = 0.3), whereas for other solutes, values obtained using icodextrin were consistently higher (P solutes is a reflection of their sieving. The increase in the MTAC of water and urea associated with an increase in convection is most likely due to increased mixing within the interstitium.

The diffusion and convection of a solute suspended in a fluid across porous membranes are known to be reduced compared to those in a bulk solution, owing to the fluid mechanical interaction between the solute and the pore wall as well as steric restriction. If the solute and the pore wall are electrically charged, the electrostatic interaction between them could affect the hindrance to diffusion and convection. In this study, the transport of charged spherical solutes through charged circular cylindrical pores filled with an electrolyte solution containing small ions was studied numerically by using a fluid mechanical and electrostatic model. Based on a mean field theory, the electrostatic interaction energy between the solute and the pore wall was estimated from the Poisson-Boltzmann equation, and the charge effect on the solute transport was examined for the solute and pore wall of like charge. The results were compared with those obtained from the linearized form of the Poisson-Boltzmann equation, i.e. the Debye-Hueckel equation. (paper)

The solid-liquid interface morphology and the micro-physical process near the moving phase boundary during natural convection melting of a horizontal layer of ice by an overlying pool of salt solution were studied experimentally. A cathetometer which amplifies the interface region was used to measure the ice melting rate. Also measured were the temperature transients of the liquid pool. Within the temperature and the density ratio ranges explored, the ice melting rate was found to be very sensitive to the ratio of pool-to-ice melt density but independent of pool-to-ice temperature difference. By varying the density ratio, three different flow regimes and morphologies of the solid-liquid interface were observed, with melt streamers emanating from the crests of the wavy interface into the pool in all three cases. The measured wavelengths (spacing) between the streamers for four different pairs of materials were correlated with the density ratio and found to agree favorably with the predictions of Taylor instability theory

Most of thermal hydraulic processes in nuclear engineering can be described by general convection-diffusion equations that are often can be simulated numerically with finite-difference method (FDM). An effective scheme for finite-difference discretization of such equations is presented in this report. The derivation of this scheme is based on analytical solutions of a simplified one-dimensional equation written for every control volume of the finite-difference mesh. These analytical solutions are constructed using linearized representations of both diffusion coefficient and source term. As a result, the Efficient Finite-Differencing (EFD) scheme makes it possible to significantly improve the accuracy of numerical method even using mesh systems with fewer grid nodes that, in turn, allows to speed-up numerical simulation. EFD has been carefully verified on the series of sample problems for which either analytical or very precise numerical solutions can be found. EFD has been compared with other popular FDM schemes including novel, accurate (as well as sophisticated) methods. Among the methods compared were well-known central difference scheme, upwind scheme, exponential differencing and hybrid schemes of Spalding. Also, newly developed finite-difference schemes, such as the the quadratic upstream (QUICK) scheme of Leonard, the locally analytic differencing (LOAD) scheme of Wong and Raithby, the flux-spline scheme proposed by Varejago and Patankar as well as the latest LENS discretization of Sakai have been compared. Detailed results of this comparison are given in this report. These tests have shown a high efficiency of the EFD scheme. For most of sample problems considered EFD has demonstrated the numerical error that appeared to be in orders of magnitude lower than that of other discretization methods. Or, in other words, EFD has predicted numerical solution with the same given numerical error but using much fewer grid nodes. In this report, the detailed

Full Text Available This paper studies the mathematical implications of the two dimensional viscous steady laminar combined free-forced convective flow of an incompressible fluid over a semi infinite fixed vertical porous plate embedded in a porous medium. It is assumed that the left surface of the plate is heated by convection from a hot fluid which is at a temperature higher than the temperature of the fluid on the right surface of the vertical plate. To achieve numerical consistency for the problem under consideration, the governing non linear partial differential equations are first transformed into a system of ordinary differential equations using a similarity variable and then solved numerically under conditions admitting similarity solutions. The effects of the physical parameters of both the incompressible fluid and the vertical plate on the dimensionless velocity and temperature profiles are studied and analysed and the results are depicted both graphically and in a tabular form. Finally, algebraic expressions and the numerical values are obtained for the local skin-friction coefficient and the local Nusselt number.

An implicit numerical technique using cubic splines is presented for solving an ablation problem on a thin wall with convective cooling. A non-uniform computational mesh with 6 grid points has been used for the numerical integration. The method has been found to be computationally efficient, providing for the care under consideration of an overall error of about 1 percent. The results obtained indicate that the convective cooling is an important factor in reducing the ablation thickness.

A technique is described which yields an accurate measurement of the temperature of density maximum of fluids which exhibit such anomalous behaviour. The method relies on the detection of changes in convective flow in a rectangular cavity containing the test fluid.The normal single-cell convection which occurs in the presence of a horizontal temperature gradient changes to a double cell configuration in the vicinity of the density maximum, and this transition manifests itself in changes in th...

The deterioration of heat transfer performance due to fouling is the prime cause for higher energy consumption and inefficiency in many industrial heat exchangers such as those in power plants, refineries, food and dairy industries. Fouling is also a very complex process in which many geometrical, physical and operating parameters are involved with poorly understood interaction. Among them, the surface roughness is an important surface characteristic that would greatly influence crystallisation fouling mechanisms and hence deposition morphology and stickability to the surface. In this work, the effect of the surface roughness of AISI 304 BA stainless steel surfaces on fouling of an aqueous solution with inverse solubility behaviour has been investigated under convective heat transfer. Several experiments have been performed on roughened surfaces ranging from 0.18 to 1.55 μm for different bulk concentrations and heat fluxes. The EDTA titration method was used to measure the concentration of the calcium sulphate salt in order to maintain it at constant value during each fouling run. Experimental results show that the heat transfer coefficient of very rough surfaces (1.55 μm) decreases more rapidly than that of 0.54 μm. Several facts contribute to this behaviour notably (1) increased of primary heterogeneous nucleation rate on the surfaces; (2) reduction of local shear stress in the valleys and (3) reduced removal rate of the crystals from the surfaces where the roughness elements protrude out of the viscous sub-layer. The results also show linear and proportional variation of the fouling rate and heat flux within the range of operating conditions. In addition, the deposition process in terms of fouling rate could only be affected at lower surface contact angles. Such results would particularly be of interest for new surface treatment technologies which aim at altering the surface texture

For in-situ studies of the formation and evolution of step patterns during the growth of protein crystals, we have designed and assembled an experimental setup based on Michelson interferometry with the surface of the growing protein crystal as one of the reflective surfaces. The crystallization part of the device allows optical monitoring of a face of a crystal growing at temperature stable within 0.05 C in a developed solution flow of controlled direction and speed. The reference arm of the interferometer contains a liquid-crystal element that allows controlled shifts of the phase of the interferograms. We employ an image processing algorithm which combines five images with a pi/2 phase difference between each pair of images. The images are transferred to a computer by a camera capable of capturing 6-8 frames per second. The device allows data collection data regarding growth over a relatively large area (approximately .3 sq. mm) in-situ and in real time during growth. The estimated dept resolution of the phase shifting interferometry is about 100 A. The lateral resolution, depending on the zoom ratio, varies between 0.3 and 0.6 micrometers. We have now collected quantitative results on the onset, initial stages and development of instabilities in moving step trains on vicinal crystal surfaces at varying supersaturation, position on the facet, crystal size and temperature with the proteins ferritin, apoferritin and thaumatin. Comparisons with theory, especially with the AFM results on the molecular level processes, see below, allow tests of the rational for the effects of convective flows and, as a particular case, the lack thereof, on step bunching.

Full Text Available Convection-diffusion problems, due to its fundamental nature, are found in various science and engineering applications. In this research, the importance of the relationship between grid structure and flow parameters in such problems is emphasized. In particular, we propose a systematic technique in the selection of the grid expansion factor based on its logarithmic relationship with low Peclet number. Such linear mathematical connection between the two non-dimensional parameters serves as a guideline for more structured decision-making and improves the heuristic process in the determination of the computational domain grid for the numerical solution of convection-diffusion equations especially in the prediction of the concentration of the scalar. Results confirm the effectiveness of the new approach.

Steam injection is widely used in heavy oil reservoirs to enhance oil recovery; elevated temperatures increase fluid mobility in several ways, but can also generate damage through shearing, crushing of weak grains, and casing impairment by shear, collapse, or buckling. Disposal of cold produced water by injection can generate thermally induced extensional fracturing, increasing the effective wellbore radius. Drilling with long open-hole sections can lead to rock temperature changes as large as 30-40 C at the casing shoe through mud heating at depth and upward mud circulation, dramatically impacting wellbore stability. Clearly, thermal stress analysis of open and cased boreholes is of primary interest for drilling and completion planning, as bottom-hole temperature changes can have as large an impact as bottom-hole pressure changes. Local wellbore stresses are the sum of far-field, pore pressure and thermally induced stresses; they may be highly inhomogeneous because of different rock properties and heat transport processes. These stresses, combined with thermal weakening and pore pressure changes, may lead to phenomena such as formation damage, sand production, shale shrinkage, and various modes of instability (shearing, spalling, fracturing, etc.). Previous studies of thermally induced stresses were primarily based on assumptions of low permeability and heat conduction only; this is inadequate when high-permeability formations are encountered. To analyze induced stresses and formation damage, a geomechanics model that is fully coupled to diffusive transport processes is employed. By assuming a constant wellbore pressure and temperature boundary condition, a closed-form solution including heat conduction and convection is obtained for the stresses near a cylindrical wellbore. The stability of an open-hole subject to non-isothermal, non-hydrostatic in situ loading and various conditions is then investigated. Our studies indicate that maximum tangential stresses are

Studies a two-dimensional natural convection in a porous, square cavity using a regular asymptotic development in powers of the Rayleigh number. Carries the approximation through to the 34th order. Analyses convergence of the resulting series for the Nusselt number in both monocellular and

Full Text Available In this article, the simultaneous convection-radiation heat transfer of a moving fin of variable thermal conductivity is studied. The differential transformation method (DTM is applied for an analytic solution for heat transfer in fin with two different profiles. Fin profiles are rectangular and exponential. The accuracy of analytic solution is validated by comparing it with the numerical solution that is obtained by fourth-order Runge-Kutta method. The analytical and numerical results are shown for different values of the embedding parameters. DTM results show that series converge rapidly with high accuracy. The results indicate that the fin tip temperature increases when ambient temperature increases. Conversely, the fin tip temperature decreases with an increase in the Peclet number, convection-conduction and radiation-conduction parameters. It is shown that the fin tip temperature of the exponential profile is higher than the rectangular one. The results indicate that the numerical data and analytical method are in a good agreement with each other.

The variational finite element method (of the Rayleigh-Ritz type) has been applied to solve the standard diffusion-convection equation of radial flow in a dispersive medium. It was shown that the imposing of the boundary condition ΔC/Δx = 0 (=null concentration gradient) introduced great errors in computation results. To remedy it this condition was imposed at the free end of the artifical domain. Its other end joined to the downstream boundary of the investigated domain. The results of calculations compared with the known analytical solutions of the parallel flow show their good accuracy. The method was used to discuss the applicability of the approximate analytical solutions of the radial flow. (author)

Highlights: • Combined convective heat and airborne transports under different flow schemes. • Natural and forced convection dominated regimes were identified with transition. • Dual solution branches were sustained for the transitional mixing flow scheme. • Rest solutions evolving from motionless flows coincided with other solution branch. • Heat and species lines were presented to delineate heat and mass transport structures. - Abstract: This paper reports a numerical study of mixed convection on a heated and polluted strip within a slot ventilated enclosure in which the displacement and mixing flow schemes are considered. Contours of streamfunction, heatfunction, and massfunction are presented to clearly scrutinize the mechanism of heat and airborne pollutant transports. For the displacement flow scheme, thermal Nusselt and pollutant Sherwood numbers under different Reynolds numbers remain almost constant as the value of Gr/Re 2 decreases down to the regime of forced convection dominated. However, as Ar increases up to the regime of natural convection dominated, both Nu and Sh increase sharply with Ar (Gr/Re 2 ). Similar trends could be observed for the situation of mixing ventilated flow scheme. In the mixing scheme, non unique steady flow solutions could be observed for the range of transitional flow regime. Upward solutions, downward solutions and rest solutions have been exemplified with varying Gr/Re 2 . Dual solution branches could be sustained at the range of 39.0 ≤ Gr/Re 2 ≤ 6.0 × 10 3 , while the rest solutions obtained from rest states were completely coinciding with former continuous solutions. The present work could be significant for the natural optimization and passive control of heat and pollutant removals from the electronic boxes or building enclosures.

Professor Jiji's broad teaching experience lead him to select the topics for this book to provide a firm foundation for convection heat transfer with emphasis on fundamentals, physical phenomena, and mathematical modelling of a wide range of engineering applications. Reflecting recent developments, this textbook is the first to include an introduction to the challenging topic of microchannels. The strong pedagogic potential of Heat Convection is enhanced by the follow ing ancillary materials: (1) Power Point lectures, (2) Problem Solutions, (3) Homework Facilitator, and, (4) Summary of Sections and Chapters.

Numerical schemes are employed to investigate heat transfer in the turbulent flow of He II. FEM is used to solve a set of equations governing the heat transfer and hydrodynamics of He II in the turbulent regime. Numerical results are compared with available experimental data and interpreted in terms of conventional heat transfer parameters such as the Prandtl number, the Peclet number, and the Nusselt number. Within the prescribed Reynolds number domain, the Gorter-Mellink thermal counterflow mechanism becomes less significant, and He II acts like an ordinary fluid. The convection heat transfer characteristics of He II in the highly turbulent regime can be successfully described by using the conventional turbulence and heat transfer theories.

The transformation group theoretic approach is applied to present an analysis of the problem of unsteady free convection flow over a continuous moving vertical sheet in an ambient fluid. The thermal boundary layer induced within a vertical semi-infinite layer of Boussinseq fluid by a constant heated bounding plate. The application of two-parameter groups reduces the number of independent variables by two, and consequently the system of governing partial differential equations with the boundary conditions reduces to a system of ordinary differential equations with appropriate boundary conditions. The obtained ordinary differential equations are solved analytically for the temperature and numerically for the velocity using the shooting method. Effect of Prandtl number on the thermal boundary-layer and velocity boundary-layer are studied and plotted in curves.

Full Text Available We study the existence and regularity of weak solutions of a phase field type model for pure material solidification in presence of natural convection. We assume that the non-stationary solidification process occurs in a two dimensional bounded domain. The governing equations of the model are the phase field equation coupled with a nonlinear heat equation and a modified Navier-Stokes equation. These equations include buoyancy forces modelled by Boussinesq approximation and a Carman-Koseny term to model the flow in mushy regions. Since these modified Navier-Stokes equations only hold in the non-solid regions, which are not known a priori, we have a free boundary-value problem.

In solution processing, functional materials are dissolved or dispersed in a solvent and deposited typically as a thin liquid film on a substrate. After evaporation of the solvent, a dry layer remains. We propose an ‘active’, non-contact technique for evaporative pattern formation that does not

Previous experimental and analytical studies of solute transport in the intervertebral disc have demonstrated that for small molecules diffusive transport alone fulfils the nutritional needs of disc cells. It has been often suggested that fluid flow into and within the disc may enhance the transport

Full Text Available The efficiency of a high-flux dialyzer in terms of buffering and toxic solute removal largely depends on the ability to use convection-diffusion mechanism inside the membrane. A two-dimensional transient convection-diffusion model coupled with acid-base correction term was developed. A finite volume technique was used to discretize the model and to numerically simulate it using MATLAB software tool. We observed that small solute concentration gradients peaked and were large enough to activate solute diffusion process in the membrane. While CO2 concentration gradients diminished from their maxima and shifted toward the end of the membrane, concentration gradients peaked at the same position. Also, CO2 concentration decreased rapidly within the first 47 minutes while optimal concentration was achieved within 30 minutes of the therapy. Abnormally high diffusion fluxes were observed near the blood-membrane interface that increased diffusion driving force and enhanced the overall diffusive process. While convective flux dominated total flux during the dialysis session, there was a continuous interference between convection and diffusion fluxes that call for the need to seek minimal interference between these two mechanisms. This is critical for the effective design and operation of high-flux dialyzers.

Recently, in Tarzia (Thermal Sci 21A:1-11, 2017) for the classical two-phase Lamé-Clapeyron-Stefan problem an equivalence between the temperature and convective boundary conditions at the fixed face under a certain restriction was obtained. Motivated by this article we study the two-phase Stefan problem for a semi-infinite material with a latent heat defined as a power function of the position and a convective boundary condition at the fixed face. An exact solution is constructed using Kummer functions in case that an inequality for the convective transfer coefficient is satisfied generalizing recent works for the corresponding one-phase free boundary problem. We also consider the limit to our problem when that coefficient goes to infinity obtaining a new free boundary problem, which has been recently studied in Zhou et al. (J Eng Math 2017. https://doi.org/10.1007/s10665-017-9921-y).

Subsurface carbon sequestration has emerged as a promising solution to the problem of increasing atmospheric carbon dioxide (CO2) levels. How does the efficiency of such a sequestration process depend on the physical and chemical characteristics of the storage site? This question is emblematic of the need to better understand the dynamics of CO2 in subsurface formations, and in particular, the properties of the convective dissolution of CO2 in the salt water of aquifers. This dissolution is known to improve the safety of the sequestration by reducing the risks of leaks of CO2 to the atmosphere. Buoyancy-driven convection makes this dissolution faster by transporting dissolved CO2 further away from the interface. Indeed, upon injection, the less dense CO2 phase rises above the aqueous layer where it starts to dissolve. The dissolved CO2 increases the density of the aqueous solution, thereby creating a layer of denser CO2-rich solution above less dense solution. This unstable density gradient in the gravity field is at the origin of convection. In this framework, we theoretically investigate the effect of CO2 pressure, salt concentration, temperature, and chemical reactions on the dissolution-driven convection of CO2 in aqueous solutions. On the basis of a linear stability analysis, we assess the stability of the time-dependent density profiles developing when CO2 dissolves in an aqueous layer below it. We predict that increasing CO2 pressure destabilizes the system with regard to buoyancy-driven convection, because it increases the density gradient at the origin of the instability. By contrast, increasing salt concentration or temperature stabilizes the system via effects on CO2 solubility, solutal expansion coefficient, diffusion coefficient and on the viscosity and density of the solution. We also show that a reaction of CO2 with chemical species dissolved in the aqueous solution can either enhance or decrease the amplitude of the convective dissolution compared

Full Text Available In this paper, triple diffusive natural convection under Darcy flow over an inclined plate embedded in a porous medium saturated with a binary base fluid containing nanoparticles and two salts is studied. The model used for the nanofluid is the one which incorporates the effects of Brownian motion and thermophoresis. In addition, the thermal energy equations include regular diffusion and cross-diffusion terms. The vertical surface has the heat, mass and nanoparticle fluxes each prescribed as a power law function of the distance along the wall. The boundary layer equations are transformed into a set of ordinary differential equations with the help of group theory transformations. A wide range of parameter values are chosen to bring out the effect of buoyancy ratio, regular Lewis number and modified Dufour parameters of both salts and nanofluid parameters with varying angle of inclinations. The effects of parameters on the velocity, temperature, solutal and nanoparticles volume fraction profiles, as well as on the important parameters of heat and mass transfer, i.e., the reduced Nusselt, regular and nanofluid Sherwood numbers, are discussed. Such problems find application in extrusion of metals, polymers and ceramics, production of plastic films, insulation of wires and liquid packaging.

Full Text Available The optimal homotopy analysis method (OHAM is employed to investigate the steady laminar incompressible free convective flow of a nanofluid past a chemically reacting upward facing horizontal plate in a porous medium taking into account heat generation/absorption and the thermal slip boundary condition. Using similarity transformations developed by Lie group analysis, the continuity, momentum, energy, and nanoparticle volume fraction equations are transformed into a set of coupled similarity equations. The OHAM solutions are obtained and verified by numerical results using a Runge-Kutta-Fehlberg fourth-fifth order method. The effect of the emerging flow controlling parameters on the dimensionless velocity, temperature, and nanoparticle volume fraction have been presented graphically and discussed. Good agreement is found between analytical and numerical results of the present paper with published results. This close agreement supports our analysis and the accuracy of the numerical computations. This paper also includes a representative set of numerical results for reduced Nusselt and Sherwood numbers in a table for various values of the parameters. It is concluded that the reduced Nusselt number increases with the Lewis number and reaction parameter whist it decreases with the order of the chemical reaction, thermal slip, and generation parameters.

An algorithm for the solution of Nernst-Planck equations with simultaneous convective flux and electric current has been developed without using Poisson's equation. The numerical simulation which has been developed reproduces the behaviour of the system employing their experimental variables as parameters of the algorithm. However, other procedures are only capable of dealing with some of the experimental conditions described here. The agreement between the theoretically predicted values and the experimentally obtained is quite reasonable. (author)

Heat transfer by natural convection and conduction in enclosures occurs in numerous practical situations including the cooling of nuclear reactors. For large temperature difference, the flow becomes compressible with a strong coupling between the continuity, the momentum and the energy equations through the equation of state, and its properties (viscosity, heat conductivity) also vary with the temperature, making the Boussinesq flow approximation inappropriate and inaccurate. There are very few reference solutions in the literature on non-Boussinesq natural convection flows. We propose here a test case problem which extends the well-known De Vahl Davis differentially heated square cavity problem to the case of large temperature differences for which the Boussinesq approximation is no longer valid. The paper is split in two parts: in this first part, we propose as yet unpublished reference solutions for cases characterized by a non-dimensional temperature difference of 0.6, Ra 10 6 (constant property and variable property cases) and Ra = 10 7 (variable property case). These reference solutions were produced after a first international workshop organized by Cea and LIMSI in January 2000, in which the above authors volunteered to produce accurate numerical solutions from which the present reference solutions could be established. (authors)

Full Text Available This review is devoted to search for Lie and Q-conditional (nonclassical symmetries and exact solutions of a class of reaction-diffusion-convection equations with exponential nonlinearities. A complete Lie symmetry classification of the class is derived via two different algorithms in order to show that the result depends essentially on the type of equivalence transformations used for the classification. Moreover, a complete description of Q-conditional symmetries for PDEs from the class in question is also presented. It is shown that all the well-known results for reaction-diffusion equations with exponential nonlinearities follow as particular cases from the results derived for this class of reaction-diffusion-convection equations. The symmetries obtained for constructing exact solutions of the relevant equations are successfully applied. The exact solutions are compared with those found by means of different techniques. Finally, an application of the exact solutions for solving boundary-value problems arising in population dynamics is presented.

This work considers the problem of steady natural convection hydromagnetic flow of a particulate suspension through an infinitely long channel in the presence of heat generation or absorption effects. The channel walls are maintained at isoflux-isothermal condition. That is, the thermal boundary conditions are such that one of the channel walls is maintained at constant heat flux while the other is maintained at a constant temperature. Various closed-form solutions of the governing equations for different special cases are obtained. A parametric study of the physical parameters involved in the problem is done to illustrate the influence of these parameters on the velocity and temperature profiles of both phases.

Full Text Available A technique is developed for evaluation of eigenvalues in solution of the differential equation d2y/dr2+(1/rdy/dr+λ2(β−r2y=0 which occurs in the problem of heat convection in laminar flow through a circular tube with silp-flow (β>1. A series solution requires the expansions of coeffecients involving extremely large numbers. No work has been reported in the case of β>1, because of its computational complexity in the evaluation of the eigenvalues. In this paper, a matrix was constructed and a computational algorithm was obtained to calculate the first four eigenvalues. Also, an asymptotic formula was developed to generate the full spectrum of eigenvalues. The computational results for various values of β were obtained.

The problem of heat and mass transfer in an unsteady free-convection flow over a continuous moving vertical sheet in an ambient fluid is investigated for constant heat flux using the group theoretical method. The nonlinear coupled partial differential equation governing the flow and the boundary conditions are transformed to a system of ordinary differential equations with appropriate boundary conditions. The obtained ordinary differential equations are solved numerically using the shooting method. The effect of Prandlt number on the velocity and temperature of the boundary-layer is plotted in curves. A comparison with previous work is presented.

Microsegregation in dentritic alloys is discussed, including solidification with and without thermal gradient, the convection of interdendritic liquid. The conservation of momentum, energy, and solute is considered. Directional solidification and thermosolutal convection are discussed.

A two dimensional mathematical model is formulated for the transitive laminar free convective, incompressible viscous fluid flow over vertical cone with variable surface heat flux combined with the effects of heat generation and absorption is considered . using a powerful computational method based on thermoelectric analogy called Network Simulation Method (NSM0, the solutions of governing nondimensionl coupled, unsteady and nonlinear partial differential conservation equations of the flow that are obtained. The numerical technique is always stable and convergent which establish high efficiency and accuracy by employing network simulator computer code Pspice. The effects of velocity and temperature profiles have been analyzed for various factors, namely Prandtl number Pr, heat flux power law exponent n and heat generation/absorption parameter Δ are analyzed graphically.

Full Text Available The two-dimensional unsteady laminar free convective heat and mass transfer fluid flow of a non-Newtonian fluid adjacent to a vertical plate has been analyzed numerically. The two parameters Lie group transformation method that transforms the three independent variables into a single variable is used to transform the continuity, the momentum, the energy and the concentration equations into a set of coupled similarity equations. The transformed equations have been solved by the Runge–Kutta–Fehlberg fourth-fifth order numerical method with shooting technique. Numerical calculations were carried out for the various parameters entering into the problem. The dimensionless velocity, temperature and concentration profiles were shown graphically and the skin friction, heat and mass transfer rates were given in tables. It is found that friction factor and heat transfer (mass transfer rate for methanol are higher (lower than those of hydrogen and water vapor. Friction factor decreases while heat and mass transfer rate increase as the Prandtl number increases. Friction (heat and mass transfer rate factor of Newtonian fluid is higher (lower than the dilatant fluid.

This article studies, an exact solution of unsteady MHD free convection boundary-layer flow of a silver nanofluid past an exponentially accelerated moving vertical plate through aporous medium in the presence of thermal radiation, transverse applied amagnetic field, radiation absorption and Heat generation or absorption with chemical reaction are investigated theoretically. We consider nanofluids contain spherical shaped nanoparticle of silverwith a nanoparticle volume concentration range smaller than or equal to 0.04. This phenomenon is modeled in the form of partial differential equations with initial boundary conditions. Some suitable dimensional variables are introduced. The corresponding dimensionless equations with boundary conditions are solved by using Laplace transform technique. The exact solutions for velocity, energy, and species are obtained, also the corresponding numerical values of nanofluid velocity, temperature and concentration profiles are represented graphically. The expressions for skin friction coefficient, the rate of heat transfer and mass transfer are derived. The present study finds applications involving heat transfer, enhancement of thermal conductivity and other applications like transportation, industrial cooling applications, heating buildings and reducing pollution, energy applications and solar absorption. The effect of heat transfer is found to be more pronounced in a silver-water nanofluid than in the other nanofluids.

A new treatment is given to the problem studied in the previous work 'Conveccao Natural em um Circuito Termico a Sodio' (1981) by the same author. It consists of another method of the solution of the energy equation. It was obtained some stability in the numerical calculation independent of the value of the step; it was also obtained a considerable reduction in the machine time. A new program is being elaborated for testing the time reduction as compared to the previous one. (author) [pt

The convective flow structures in the vapor phase on earth are shown to be single unicellular, indicating the solutally dominant convection is important. These findings reflect that the total molar fluxes show asymmetrical patterns in a viewpoint of interfacial distributions. With decreasing the gravitational level form 1 g{sub 0} down to 1.0x10{sup -4} g{sub 0}, the total molar fluxes decay first order exponentially. It is also found that the total molar fluxes decay first order exponentially with increasing the partial pressure of component B, PB (Torr) form 5 Torr up to 400 Torr.. Under microgravity environments less than 1 g{sub 0}, a diffusive-convection mode is dominant and, results in much uniformity in front of the crystal regions in comparisons with a normal gravity acceleration of 1 g{sub 0}.

Full Text Available The unsteady free flow of a Casson fluid past an oscillating vertical plate with constant wall temperature has been studied. The Casson fluid model is used to distinguish the non-Newtonian fluid behaviour. The governing partial differential equations corresponding to the momentum and energy equations are transformed into linear ordinary differential equations by using nondimensional variables. Laplace transform method is used to find the exact solutions of these equations. Expressions for shear stress in terms of skin friction and the rate of heat transfer in terms of Nusselt number are also obtained. Numerical results of velocity and temperature profiles with various values of embedded flow parameters are shown graphically and their effects are discussed in detail.

The current analysis reports the untapped characteristics of magneto-hydrodynamic dual convection boundary layer stagnation point flow of Powell-Eyring fluid by way of cylindrical surface. Flow exploration is carried out with the combined effects of thermal and solutal stratification. The strength of temperature and concentration adjacent to the cylindrical surface is assumed to be greater than the ambient fluid. Flow conducting mathematically modelled equations are fairly transformed into system of coupled non-linear ordinary differential equations with the aid of suitable transformations. The computations are made against these resultant coupled equations through shooting technique by the support of fifth order Runge-Kutta algorithm. A parametric study is performed to examine the effect logs of various pertinent flow controlling parameters on the velocity, temperature and concentration flow regime. The achieved outcomes are validated by developing comparison with existing published literature. In addition, numerical values of skin friction coefficient and Nusselt number are presented graphically for two different geometries namely, plate and cylinder.

A deterministic particle-tracking code (TRACK3D) has been developed to compute convective flow paths of conservative (nonreactive) contaminants through porous geological media. TRACK3D requires the groundwater velocity distribution, which, in our applications, results from flow simulations using AECL`s MOTIF code. The MOTIF finite-element code solves the transient and steady-state coupled equations of groundwater flow, solute transport and heat transport in fractured/porous media. With few modifications, TRACK3D can be used to analyse the velocity distributions calculated by other finite-element or finite-difference flow codes. This report describes the assumptions, limitations, organization, operation and applications of the TRACK3D code, and provides a comprehensive user`s manual.

In considering the large scale stellar convection problem the outer layers of a star are modelled as two co-rotating plane layers coupled at a fluid/fluid interface. Heating from below causes only the upper fluid to convect, although this convection can penetrate into the lower fluid. Stability analysis is then used to find the most unstable mode of convection. With parameters appropriate to the Sun the most unstable mode is steady convection in thin cells (aspect ratio {approx equal} 0.2) filling the convection zone. There is negligible vertical motion in the lower fluid, but considerable thermal penetration, and a large jump in helicity at the interface, which has implications for dynamo theory. An {alpha}{omega} dynamo is investigated in isolation from the convection problem. Complexity is included by allowing both latitudinal and time dependence in the magnetic fields. The nonlinear dynamics of the resulting partial differential equations are analysed in considerable detail. On varying the main control parameter D (the dynamo number), many transitions of behaviour are found involving many forms of time dependence, but not chaos. Further, solutions which break equatorial symmetry are common and provide a theoretical explanation of solar observations which have this symmetry. Overall the behaviour was more complicated than expected. In particular, there were multiple stable solutions at fixed D, meaning that similar stars can have very different magnetic patterns, depending upon their history. (author).

Written by an internationally recognized authority on heat transfer and thermodynamics, this second edition of Convection Heat Transfer contains new and updated problems and examples reflecting real-world research and applications, including heat exchanger design. Teaching not only structure but also technique, the book begins with the simplest problem solving method (scale analysis), and moves on to progressively more advanced and exact methods (integral method, self similarity, asymptotic behavior). A solutions manual is available for all problems and exercises.

Thermo convective instabilities in horizontal fluid layers are discussed with emphasis on the Rayleigh-Bernard model problem. Steady solutions and time-dependent phenomena (relaxation oscillations and transition to turbulence) are studied within the nonlinear Boussinesq-Oberbeck approximation. Homogeneous steady solutions, limit cycles, and inhomogeneous (ordered) spatial structures are also studied in simple reaction-diffusion systems. Lastly, the non-periodic attractor that appears at large Rayleigh numbers in the truncated Boussinesq-Oberbeck model of Lorenz, is constructed, and a discussion of turbulent behavior is given. (Author) 105 refs.

Thermo convective instabilities in horizontal fluid layers are discussed with emphasis on the Rayleigh-Bernard model problem. Steady solutions and time-dependent phenomena (relaxation oscillations and transition to turbulence) are studied within the nonlinear Boussinesq-Oberbeck approximation. Homogeneous steady solutions, limit cycles, and inhomogeneous (ordered) spatial structures are also studied in simple reaction-diffusion systems. Lastly, the non-periodic attractor that appears at large Rayleigh numbers in the truncated Boussinesq-Oberbeck model of Lorenz, is constructed, and a discussion of turbulent behavior is given. (Author) 105 refs

National Oceanic and Atmospheric Administration, Department of Commerce — Current convective hazards identified by the National Convective Weather Detection algorithm. The National Convective Weather Diagnostic (NCWD) is an automatically...

QUICKER scheme has several attractive properties. However, under highly convective conditions, it produces overshoots and possibly some oscillations on each side of steps in the dependent variable when the flow is convected at an angle oblique to the grid line. Fortunately, it is possible to modify the QUICKER scheme using non-linear and linear functional relationship. Details of the development of polynomial upwinding scheme are given in this paper, where it is seen that this non-linear scheme has also third order accuracy. This polynomial upwinding scheme is used as the basis for the SHARPER and SMARTER schemes. Another revised scheme was developed by partial modification of QUICKER scheme using CDS and UPWIND schemes (QUICKUP). These revised schemes are tested at the well known bench mark flows, Two-Dimensional Pure Convection Flows in Oblique-Step, Lid Driven Cavity Flows and Buoyancy Driven Cavity Flows. For remain absolutely monotonic without overshoot and oscillation. QUICKUP scheme is more accurate than any other scheme in their relative accuracy. In high Reynolds number Lid Driven Catity Flow, SMARTER and SHARPER schemes retain lower computational cost than QUICKER and QUICKUP schemes, but computed velocity values in the revised schemes produced less predicted values than QUICKER scheme which is strongly effected by overshoot and undershoot values. Also, in Buoyancy Driven Cavity Flow, SMARTER, SHARPER and QUICKUP schemes give acceptable results. (Author)

We propose a numerical solution for the adjoint operator of a forced convection heat transfer problem to evaluate mean heat transfer characteristics under arbitrary thermal conditions. Using the numerical solutions of the adjoint problems under Dirichlet and Neumann conditions, both of which can be computed using a conventional CFD code, the influence function of the local surface temperature on the total heat transfer and that of the local surface heat flux on the mean surface temperature are obtained. As a result, the total heat fluxes for arbitrary surface temperature distributions and the mean surface temperatures for arbitrary surface heat flux distributions can be calculated using these influence functions. The influence functions for a circular cylinder and for an in-line square rod array are presented. 14 refs., 9 figs., 1 tab.

It has been established by MRI visualization experiments that the convection of nanoparticles and large molecules with high rate of water flow in the vitreous humor will experience resistance, depending on the respective permeabilities of the injected solute. A set of experiments conducted with Gd-DTPA (Magnevist, Bayer AG, Leverkusen, Germany) and 30 nm gadolinium-based particles (Gado CELLTrackTM, Biopal, Worcester, MA) as MRI contrast agents showed that the degree of convective transport in this Darcy-type porous medium varies between the two solutes. These experiments consisted of injecting a mixture of the two (a 30 μl solution of 2% Magnevist and 1% nanoparticles) at the middle of the vitreous of an ex vivo whole bovine eye and subjecting the vitreous to water flow rate of 100 μl/min. The water (0.9% saline solution) was injected at the top of the eye, and was allowed to drain through small slits cut at the bottom of the eyeball. After 50 minutes of pumping, MRI images showed that the water flow carried the Gd-DTPA farther than the nanoparticles, even though the two solutes, being mixed, were subjected to the same convective flow conditions. We find that the convectedsolute lags the water flow, depending on the solute permeability. The usual convection term needs to be adjusted to allow for the filtration effect on the larger particles in the form (1- σ) u . ∇ c with important implications for the modeling of such systems.

Full Text Available The aim of the present study is to investigate the influence of non-uniform heat source/sink, mass transfer and chemical reaction on an unsteady mixed convection boundary layer flow of a magneto-micropolar fluid past a stretching/shrinking sheet in the presence of viscous dissipation and suction/injection. The governing equations of the flow, heat and mass transfer are transformed into system of nonlinear ordinary differential equations by using similarity transformation and then solved numerically using Shooting technique with Matlab Package. The influence of non-dimensional governing parameters on velocity, microrotation, temperature and concentration profiles are discussed and presented with the help of their graphical representations. Also, friction factor, heat and mass transfer rates have been computed and presented through tables. Under some special conditions, present results are compared with the existed results to check the accuracy and validity of the present study. An excellent agreement is observed with the existed results.

We numerically investigate a mixed convection model for a magnetohydrodynamic (MHD) Jeffery fluid flowing over an exponentially stretching sheet. The influence of thermal radiation and chemical reaction is also considered in this study. The governing non-linear coupled partial differential equations are reduced to a set of coupled non-linear ordinary differential equations by using similarity functions. This new set of ordinary differential equations are solved numerically using the Spectral Quasi-Linearization Method. A parametric study of physical parameters involved in this study is carried out and displayed in tabular and graphical forms. It is observed that the velocity is enhanced with increasing values of the Deborah number, buoyancy and thermal radiation parameters. Furthermore, the temperature and species concentration are decreasing functions of the Deborah number. The skin friction coefficient increases with increasing values of the magnetic parameter and relaxation time. Heat and mass transfer rates increase with increasing values of the Deborah number and buoyancy parameters.

National Oceanic and Atmospheric Administration, Department of Commerce — The NCWF is an automatically generated depiction of: (1) current convection and (2) extrapolated signficant current convection. It is a supplement to, but does NOT...

Full Text Available A theoretical and numerical study is presented to analyze the nonlinear, non-isothermal, magnetohydrodynamic (MHD free convection boundary layer flow and heat transfer in a non-Darcian, isotropic, homogenous porous medium, in the presence of Hall currents, Ionslip currents, viscous heating and Joule heating. A power-law variation is used for the temperature at the wall. The governing nonlinear coupled partial differential equations for momentum conservation in the x and z directions and heat conservation, in the flow regime are transformed from an (x, y, z coordinate system to a (ξ,η coordinate system in terms of dimensionless x-direction velocity (∂F/∂η and z-direction velocity (G and dimensionless temperature function (H under appropriate boundary conditions. Both Darcian and Forchheimer porous impedances are incorporated in both momentum equations. Computations are also provided for the variation of the x and z direction shear stress components and also local Nusselt number. Excellent correlation is achieved with a Nakamura tridiagonal finite difference scheme (NTM. The model finds applications in magnetic materials processing, MHD power generators and purification of crude oils.

Solution is given to a number of problems of free convection in incompressible viscous fluid in elementary macrocapillaries with nonuniform temperature distribution at the boundary. The fluid flow structure and effect of a magnetic field on convection in the case of conducting fluid has been studied in detail. The influence of macrocapillary properties on the flow structure, rate of convection, and temperature distribution has been estimated.

A similar solution for the flow past a vertical plate started impulsively in its own plane in a viscous incompressible fluid is presented on taking into account the effects of variable suction and/or injection and mass transfer. To solve the momentum, energy and concentration equations, a time dependent length scale is introduced, which leads to the driving parameters γ(=G r /R σ 2 ) and γ*(=G r */R σ 2 ), where G r and G r * are respectively the Grashof and modified Grashof numbers while R σ is the Reynolds number. The resulting locally similar momentum equation is then solved by the method of superposition. The effects of the parameters and that of suction/injection on the flow and on the wall shear-stress of the plate are shown graphically for different values of Schmidt number and transpiration parameter. (author). 24 refs, 11 figs

Convective self-aggregation, the spontaneous organization of initially scattered convection into isolated convective clusters despite spatially homogeneous boundary conditions and forcing, was first recognized and studied in idealized numerical simulations. While there is a rich history of observational work on convective clustering and organization, there have been only a few studies that have analyzed observations to look specifically for processes related to self-aggregation in models. Here we review observational work in both of these categories and motivate the need for more of this work. We acknowledge that self-aggregation may appear to be far-removed from observed convective organization in terms of time scales, initial conditions, initiation processes, and mean state extremes, but we argue that these differences vary greatly across the diverse range of model simulations in the literature and that these comparisons are already offering important insights into real tropical phenomena. Some preliminary new findings are presented, including results showing that a self-aggregation simulation with square geometry has too broad distribution of humidity and is too dry in the driest regions when compared with radiosonde records from Nauru, while an elongated channel simulation has realistic representations of atmospheric humidity and its variability. We discuss recent work increasing our understanding of how organized convection and climate change may interact, and how model discrepancies related to this question are prompting interest in observational comparisons. We also propose possible future directions for observational work related to convective aggregation, including novel satellite approaches and a ground-based observational network.

The effects of magnetic field and temperature heat source on the free and forced convection flow past an infinite vertical plate is studied analytically. Solutions of the reduced equation appropriate in the forced convection and free convection regime are obtained using perturbation technique. The expression for the velocity field, skin friction and Nusselt number have been obtained

The book describes results of investigations of a series of convective heat and mass transfer problems in rotating-disk systems. Methodology used included integral methods, self-similar and approximate analytical solutions, as well as CFD.

The present work deals with the steady laminar three-dimensional mixed convective magnetohydrodynamic (MHD) boundary layer flow of Casson nanofluid over a bidirectional stretching surface. A uniform magnetic field is applied normal to the flow direction. Similarity variables are implemented to convert the non-linear partial differential equations into ordinary ones. Convective boundary conditions are utilized at surface of the sheet. A numerical technique of Runge–Kutta–Fehlberg (RFK45) is used to obtain the results of velocity, temperature and concentration fields. The physical dimensionless parameters are discussed through tables and graphs. - Highlights: • Mixed convective boundary layer flow of Casson nanofluid is taken into account. • Impact of magnetic field is examined. • Convective heat and mass conditions are imposed. • Numerical solutions are presented and discussed.

Intended for readers who have taken a basic heat transfer course and have a basic knowledge of thermodynamics, heat transfer, fluid mechanics, and differential equations, Convective Heat Transfer, Third Edition provides an overview of phenomenological convective heat transfer. This book combines applications of engineering with the basic concepts of convection. It offers a clear and balanced presentation of essential topics using both traditional and numerical methods. The text addresses emerging science and technology matters, and highlights biomedical applications and energy technologies. What’s New in the Third Edition: Includes updated chapters and two new chapters on heat transfer in microchannels and heat transfer with nanofluids Expands problem sets and introduces new correlations and solved examples Provides more coverage of numerical/computer methods The third edition details the new research areas of heat transfer in microchannels and the enhancement of convective heat transfer with nanofluids....

Full Text Available Convective processes profoundly affect the global water and energy balance of our planet but remain a challenge for global climate modeling. Here we develop and investigate the suitability of a unified convection scheme, capable of handling both shallow and deep convection, to simulate cases of tropical oceanic convection, mid-latitude continental convection, and maritime shallow convection. To that aim, we employ large-eddy simulations (LES as a benchmark to test and refine a unified convection scheme implemented in the Single-column Community Atmosphere Model (SCAM. Our approach is motivated by previous cloud-resolving modeling studies, which have documented the gradual transition between shallow and deep convection and its possible importance for the simulated precipitation diurnal cycle. Analysis of the LES reveals that differences between shallow and deep convection, regarding cloud-base properties as well as entrainment/detrainment rates, can be related to the evaporation of precipitation. Parameterizing such effects and accordingly modifying the University of Washington shallow convection scheme, it is found that the new unified scheme can represent both shallow and deep convection as well as tropical and mid-latitude continental convection. Compared to the default SCAM version, the new scheme especially improves relative humidity, cloud cover and mass flux profiles. The new unified scheme also removes the well-known too early onset and peak of convective precipitation over mid-latitude continental areas.

for asteroseismology, because of the challenges inherent in modelling turbulent convection in 1D stellar models. As a result of oversimplifying the physics near the surface, theoretical calculations systematically overestimate the oscillation frequencies. This has become known as the asteroseismic surface effect. Due...... to lacking better options, this frequency difference is typically corrected for with ad-hoc formulae. The topic of this thesis is the improvement of 1D stellar convection models and the effects this has on asteroseismic properties. The source of improvements is 3D simulations of radiation...... atmospheres to replace the outer layers of stellar models. The additional turbulent pressure and asymmetrical opacity effects in the atmosphere model, compared to convection in stellar evolution models, serve to expand the atmosphere. The enlarged acoustic cavity lowers the pulsation frequencies bringing them...

Using stability theory, numerical simulations, and in some instances experiments, it is demonstrated that the critical Rayleigh number for the bifurcation (1) from the no-motion (conduction) state to the motion state and (2) from time-independent convection to time-dependent, oscillatory convection in the thermal convection loop and Rayleigh-Benard problems can be significantly increased or decreased. This is accomplished through the use of a feedback controller effectuating small perturbations in the boundary data. The controller consists of sensors which detect deviations in the fluid`s temperature from the motionless, conductive values and then direct actuators to respond to these deviations in such a way as to suppress the naturally occurring flow instabilities. Actuators which modify the boundary`s temperature/heat flux are considered. The feedback controller can also be used to control flow patterns and generate complex dynamic behavior at relatively low Rayleigh numbers.

The experimental work includes developing and using a thermal convection cell to obtain measurements of the heat flux and turbulent core temperature of a horizontal layer of fluid heated internally and subject to both stabilizing and destabilizing temperature differences. The ranges of Rayleigh numbers tested were 10 7 equal to or less than R/sub I/ equal to or less than 10 13 and -10 10 equal to or less than R/sub E/ equal to or less than 10 10 . Power integral methods were found to be adequate for interpolating and extrapolating the data. The theoretical work consists of the derivation, solution and use of the mean field equations for study of thermally driven convection in horizontal layers of infinite extent. The equations were derived by a separation of variables technique where the horizontal directions were described by periodic structures and the vertical being some function of z. The derivation resulted in a coupled set of momentum and energy equations. The equations were simplified by using the infinite Prandtl number limit and neglecting direct intermodal interaction. Solutions to these equations are used to predict the existence of multi-wavenumber flows at all supercritical Rayleigh numbers. Subsequent inspection of existing experimental photographs of convecting fluids confirms their existence. The onset of time dependence is found to coincide with the onset of the second convective mode. Each mode is found to consist of two wavenumbers and typically the velocity and temperature fields of the right modal branch are found to be out of phase

This study is an experimental investigation of variable density groundwater flow in homogeneous and lenticular porous media. A solution of 500 mg/l Rhodamine WT dye served as the carrier for various concentrations of solute (NaCl) introduced into a two-dimensional flow tank at concentrations ranging from 1000 to 100,000 mg/l. At the scale of the experiments, mass transport depends upon both forced and free convection. In addition, density differences as low as 0.008 g/cm 3 (1000 mg/l NaCl) between a plume of dense water and ambient groundwater in homogeneous medium produces gravitational instabilities at realistic groundwater velocities. These instabilities are manifest by lobe-shaped protuberances that formed first along the bottom edge of the plume and later within the plume. As the density difference increases to 0.0015 g/cm 3 (2000 mg/l NaCl), 0.0037 g/cm 3 (5000 mg/l NaCl) or higher, this unstable mixing due to convective dispersion significantly alters the spreading process, resulting in a large degree of vertical spreading of the plume. In a lenticular medium the combination of convective dispersion and nonuniform flow due to heterogeneities results in relatively large dispersion. Scale considerations indicate that convective dispersion may provide an important component of mixing at the field scale. (Author) (30 refs., 12 figs., 3 tabs.)

Scrape-off-layer (SOL) convection in fusion experiments appears to be a universal phenomenon that can 'short-circuit' the divertor in some cases. The theory of 'blob' transport provides a simple and robust physical paradigm for studying convective transport. This paper summarizes recent advances in the theory of blob transport and its comparison with 2D and 3D computer simulations. We also discuss the common physical basis relating radial transport of blobs, pellets, and ELMs and a new blob regime that may lead to a connection between blob transport and the density limit. (author)

We review recent progress using numerical simulations as a testbed for development of a theory of stellar convection, much as envisaged by John von Newmann. Necessary features of the theory, non-locality and fluctuations, are illustrated by computer movies. It is found that the common approximation of convection as a diffusive process presents the wrong physical picture, and improvements are suggested. New observational results discussed at the conference are gratifying in their validation of some of our theoretical ideas, especially the idea that SNIb and SNIc events are related to the explosion of massive star cores which have been stripped by mass loss and binary interactions [1

Full Text Available Lateral mixing parameters in buoyancy-driven deep convection schemes are among the most sensitive and important unknowns in atmosphere models. Unfortunately, there is not a true optimum value for plume mixing rate, but rather a dilemma or tradeoff: Excessive dilution of updrafts leads to unstable stratification bias in the mean state, while inadequate dilution allows deep convection to occur too easily, causing poor space and time distributions and variability. In this too-small parameter space, compromises are made based on competing metrics of model performance. We attempt to escape this “entrainment dilemma” by making bulk plume parameters (chiefly entrainment rate depend on a new prognostic variable (“organization,” org meant to reflect the rectified effects of subgrid-scale structure in meteorological fields. We test an org scheme in the Community Atmosphere Model (CAM5 with a new unified shallow-deep convection scheme (UW-ens, a 2-plume version of the University of Washington scheme. Since buoyant ascent involves natural selection, subgrid structure makes convection systematically deeper and stronger than the pure unorganized case: plumes of average (or randomly sampled air rising in the average environment. To reflect this, org is nonnegative, but we leave it dimensionless. A time scale characterizes its behavior (here ∼3 h for a 2o model. Currently its source is rain evaporation, but other sources can be added easily. We also let org be horizontally transported by advection, as a mass-weighted mean over the convecting layer. Linear coefficients link org to a plume ensemble, which it assists via: 1 plume base warmth above the mean temperature 2 plume radius enhancement (reduced mixing, and 3 increased probability of overlap in a multi-plume scheme, where interactions benefit later generations (this part has only been implemented in an offline toy column model. Since rain evaporation is a source for org, it functions as a time

Phenomena of convection are abundant in nature as well as in industry. This volume addresses the subject of convection from the point of view of both, theory and application. While the first three chapters provide a refresher on fluid dynamics and heat transfer theory, the rest of the book describes the modern developments in theory. Thus it brings the reader to the ""front"" of the modern research. This monograph provides the theoretical foundation on a topic relevant to metallurgy, ecology, meteorology, geo-and astrophysics, aerospace industry, chemistry, crystal physics, and many other fiel

To investigate the real-world relevance of idealized-model convective self-aggregation, five 15-day cases of real organized convection in the tropics are simulated. These include multiple simulations of each case to test sensitivities of the convective organization and mean states to interactive radiation, interactive surface fluxes, and evaporation of rain. These simulations are compared to self-aggregation seen in the same model configured to run in idealized radiative-convective equilibriu...

This book presents a new algorithm to calculate fluid flow and heat transfer of laminar mixed convection. It provides step-by-step tutorial help to learn quickly how to set up the theoretical and numerical models of laminar mixed convection, to consider the variable physical properties of fluids, to obtain the system of numerical solutions, to create a series of formalization equations for the convection heat transfer by using a curve-fitting approach combined with theoretical analysis and derivation. It presents the governing ordinary differential equations of laminar mixed convection, equivalently transformed by an innovative similarity transformation with the description of the related transformation process. A system of numerical calculations of the governing ordinary differential equations is presented for the water laminar mixed convection. A polynomial model is induced for convenient and reliable treatment of variable physical properties of liquids. The developed formalization equations of mixed convec...

Numerous observations provide evidence that the standard picture, in which convective mixing is limited to the unstable layers of a star, is incomplete. The mixing layers in real stars are significantly more extended than what the standard models predict. Some of the observations require changing

Full Text Available This paper aims to renew interest on mixed thermal convection research and to emphasize three issues that arise from the present analysis: (i a clear definition of the reference temperature in the Boussinesq approximation; (ii a practical delimitation of the three convective modes, which are the forced convection (FC, mixed convection (MC and natural (or free convection (NC; (iii and, finally, a uniform description of the set FC/MC/NC in the similarity framework. The planar case, for which analytical solutions are available, allows a detailed illustration of the answers here advanced to the above issues.

Observed equatorial wave propagation is intimately linked to convective organization and it's coupling to features of the larger-scale flow. In this talk we a use simple 4 level model to accommodate vertical modes of a mass flux convection scheme (shallow, mid-level and deep). Two paradigms of convection are used to represent convective processes. One that has only both random (unorganized) diagnosed fluctuations of convective properties and one with organized fluctuations of convective properties that are amplified by previously existing convection and has an explicit moistening impact on the local convecting environment We show a series of model simulations in single-column, 2D and 3D configurations, where the role of convective organization in wave propagation is shown to be fundamental. For the optimal choice of parameters linking organization to local atmospheric state, a broad array of convective wave propagation emerges. Interestingly the key characteristics of propagating modes are the low-level moistening followed by deep convection followed by mature 'large-scale' heating. This organization structure appears to hold firm across timescales from 5-day wave disturbances to MJO-like wave propagation.

The effect of Brinkman number and magnetic field on laminar convection in a vertical plate channel with uniform and asymmetric temperatures has been studied. The dimensionless form of momentum and energy balanced equations has been solved using one term perturbation series solution. The solution of the ...

The Petrov-Galerkin method is adaptively applied to convection dominated problems. To this end a feedback function is created which increases the control of derivatives in the direction of he gradient of the approximate solution. This leads to a method with good stability properties close to boundary layers and high accuracy in those regions where regular solutions do occur. (author) [pt

Magnetospheric physics, which grew out of attempts to understand the space environment of the Earth, is becoming increasingly applicable to other systems in the Universe. Among the planets, in addition to the Earth, Jupiter, Mercury, Mars and (in a somewhat different way) Venus are now known to have magnetospheres. The magnetospheres of pulsars have been regarded as an essential part of the pulsar phenomenon. Other astrophysical systems, such as supernova remnant shells or magnetic stars and binary star systems, may be describable as magnetospheres. The major concepts of magnetospheric physics thus need to be formulated in a general way not restricted to the geophysical context in which they may have originated. Magnetospheric convection has been one of the most important and fruitful concepts in the study of the Earth's magnetosphere. This paper describes the basic theoretical notions of convection in a manner applicable to magnetospheres generally and discusses the relative importance of convective corotational motions, with particular reference to the comparison of the Earth and Jupiter. (Auth.)

Heat or mass transfer around an evaporating drop or condensing vapor bubble is a complex issue due to the interplay between the substrate properties, diffusion- and convection-driven mass transfer, and Marangoni effects, to mention but a few. In order to disentangle these mechanisms, we focus here mainly on the convective mass transfer contribution in an isothermal mass transfer problem. For this, we study the case of a millimetric carbon dioxide bubble which is suspended under a substrate and dissolved into pure liquid water. The high solubility of CO2 in water makes the liquid denser and promotes a buoyant-driven flow at a high (solutal) Rayleigh number (Ra˜104 ). The alteration of p H allows the concentration field in the liquid to be imaged by laser fluorescence enabling us to measure both the global mass flux (bubble volume, contact angle) and local mass flux around the bubble along time. After a short period of mass diffusion, where the boundary layer thickens like the square root of time, convection starts and the CO2 is carried by a plume falling at constant velocity. The boundary layer thickness then reaches a plateau which depends on the bubble cross section. Meanwhile the plume velocity scales like (dV /d t )1 /2 with V being the volume of the bubble. As for the rate of volume loss, we recover a constant mass flux in the diffusion-driven regime followed by a decrease in the volume V like V2 /3 after convection has started. We present a model which agrees well with the bubble dynamics and discuss our results in the context of droplet evaporation, as well as high Rayleigh convection.

Natural convection in low aspect ratio rectangular enclosures is considered along with three-dimensional convection within rectangular boxes, natural convection flow visualization in irradiated water cooled by air flow over the surface, free convection in vertical slots, the stratification in natural convection in vertical enclosures, the flow structure with natural convection in inclined air-filled enclosures, and natural convection across tilted, rectangular enclosures of small aspect ratio. Attention is given to the effect of wall conduction and radiation on natural convection in a vertical slot with uniform heat generation of the heated wall, a numerical study of thermal insulation enclosure, free convection in a piston-cylinder enclosure with sinusoidal piston motion, natural convection heat transfer between bodies and their spherical enclosure, an experimental study of the steady natural convection in a horizontal annulus with irregular boundaries, three-dimensional natural convection in a porous medium between concentric inclined cylinders, a numerical solution for natural convection in concentric spherical annuli, and heat transfer by natural convection in porous media between two concentric spheres

A model is presented for thermal convection in an inclined layer of porous material when the medium has a bidispersive structure. Thus, there are the usual macropores which are full of a fluid, but there are also a system of micropores full of the same fluid. The model we employ is a modification of the one proposed by Nield & Kuznetsov (2006 Int. J. Heat Mass Transf. 49, 3068–3074. (doi:10.1016/j.ijheatmasstransfer.2006.02.008)), although we consider a single temperature field only. PMID:27616934

Full Text Available In the present paper, the effect of solar radiation on automobiles has been studied by both experimentally and numerically. The numerical solution is done by an operation friendly and fast CFD code – SC/Tetra with a full scale model of a SM3 car and turbulence is modeled by the standard k-ε equation. Numerical analysis of the three-dimensional model predicts a detailed description of fluid flow and temperature distribution in the passenger compartment during both the natural convection due to the incoming solar radiation and mixed convection due to the flow from defrost nozzle and radiation. It can be seen that solar radiation is an important parameter to raise the compartment temperature above the ambient temperature during summer. During natural convection, the rate of heat transfer is fast at the initial period. In the mixed convection analyses, it is found that the temperature drops down to a comfortable range almost linearly at the initial stage. Experimental investigations are performed to determine the temperature contour on the windshield and the local temperature at a particular point for further validation of the numerical results.

Convection in Porous Media, 4th Edition, provides a user-friendly introduction to the subject, covering a wide range of topics, such as fibrous insulation, geological strata, and catalytic reactors. The presentation is self-contained, requiring only routine mathematics and the basic elements of fluid mechanics and heat transfer. The book will be of use not only to researchers and practicing engineers as a review and reference, but also to graduate students and others entering the field. The new edition features approximately 1,750 new references and covers current research in nanofluids, cellular porous materials, strong heterogeneity, pulsating flow, and more. Recognized as the standard reference in the field Includes a comprehensive, 250-page reference list Cited over 2300 times to date in its various editions Serves as an introduction for those entering the field and as a comprehensive reference for experienced researchers Features new sections on nanofluids, carbon dioxide sequestration, and applications...

Warm air aloft is stable. This explains the lack of strong winds in a warm front and how nighttime radiative cooling can lead to motionless air that can trap smog. The stability of stratospheric air can be attributed to the fact that it is heated from above as ultraviolet radiation strikes the ozone layer. On the other hand, fluid heated from below is unstable and can lead to Bernard convection cells. This explains the generally turbulent nature of the troposphere, which receives a significant fraction of its heat directly from the Earth's warmer surface. The instability of cold fluid aloft explains the violent nature of a cold front, as well as the motion of Earth's magma, which is driven by radioactive heating deep within the Earth's mantle. This paper describes how both effects can be demonstrated using four standard beakers, ice, and a bit of food coloring.

This book provides a user-friendly introduction to the topic of convection in porous media The authors as- sume that the reader is familiar with the basic elements of fluid mechanics and heat transfer, but otherwise the book is self-contained The book will be useful both as a review (for reference) and as a tutorial work, suitable as a textbook in a graduate course or seminar The book brings into perspective the voluminous research that has been performed during the last two decades The field has recently exploded because of worldwide concern with issues such as energy self-sufficiency and pollution of the environment Areas of application include the insulation of buildings and equipment, energy storage and recovery, geothermal reservoirs, nuclear waste disposal, chemical reactor engineering, and the storage of heat-generating materials such as grain and coal Geophysical applications range from the flow of groundwater around hot intrusions to the stability of snow against avalanches

Full Text Available In this paper, we propose a fitted numerical method for solving convection delayed dominated diffusion equation. A fitting factor is introduced and the model equation is discretized by cubic spline method. The error analysis is analyzed for the consider problem. The numerical examples are solved using the present method and compared the result with the exact solution.

Radial curvature effects on axisymmetric free convection boundary-layer flow are investigated for vertical cylinders and cones for some special non-uniform temperature differences between the surface and the ambient fluid. The solution is given as a power series expansion, the first term being equal

The problem of magnetohydrodynamic free convection of an electrically conducting fluid in a strong cross field is investigated. It is solved by using a singular perturbation technique. The solutions presented cover the range of Prandtl numbers from zero to order one. This includes both the important

The Rayleigh-Benard convection in the microemulsion consisting of water (7.5%), cyclohexan (oil-61.7%) and diethylenglycolmonobutylether (surfactant-30.8%) is studied from the onset of convection to the phase separation. The five classes of convection patterns are observed and recorded on the video: localized travelling waves, travelling waves, travelling waves and localized steady rolls, steady rolls and steady polygons. The Fourier transforms and histograms of these patterns are presented. The origin of any pattern is discussed. The intermittent behaviour close to the phase separation was observed. Possible applications of the obtained results are suggested. (author). 6 refs, 4 figs

In a recent paper published in this Journal the title problem has been investigated numerically. In the present paper the exact solution for the temperature boundary layer is given in terms of the solution of the flow problem (the Blasius problem) in a compact integral form.

A convective heat flow probe device is provided which measures heat flow and fluid flow magnitude in the formation surrounding a borehole. The probe comprises an elongate housing adapted to be lowered down into the borehole; a plurality of heaters extending along the probe for heating the formation surrounding the borehole; a plurality of temperature sensors arranged around the periphery of the probe for measuring the temperature of the surrounding formation after heating thereof by the heater elements. The temperature sensors and heater elements are mounted in a plurality of separate heater pads which are supported by the housing and which are adapted to be radially expanded into firm engagement with the walls of the borehole. The heat supplied by the heater elements and the temperatures measured by the temperature sensors are monitored and used in providing the desired measurements. The outer peripheral surfaces of the heater pads are configured as segments of a cylinder and form a full cylinder when taken together. A plurality of temperature sensors are located on each pad so as to extend along the length and across the width thereof, with a heating element being located in each pad beneath the temperature sensors. An expansion mechanism driven by a clamping motor provides expansion and retraction of the heater pads and expandable packer-type seals are provided along the probe above and below the heater pads.

Water vapor is lighter than air; this can enhance water evaporation by triggering vapor convection but there is little evidence. We directly visualize evaporation of nanoliter (2 to 700 nL) water droplets resting on silicon wafer in calm air using a high-resolution dual X-ray imaging method. Temporal evolutions of contact radius and contact angle reveal that evaporation rate linearly changes with surface area, indicating convective (instead of diffusive) evaporation in nanoliter water droplet...

Full Text Available A review of conjugate convective heat transfer problems solved during the early and current time of development of this modern approach is presented. The discussion is based on analytical solutions of selected typical relatively simple conjugate problems including steady-state and transient processes, thermal material treatment, and heat and mass transfer in drying. This brief survey is accompanied by the list of almost two hundred publications considering application of different more and less complex analytical and numerical conjugate models for simulating technology processes and industrial devices from aerospace systems to food production. The references are combined in the groups of works studying similar problems so that each of the groups corresponds to one of selected analytical solutions considered in detail. Such structure of review gives the reader the understanding of early and current situation in conjugate convective heat transfer modeling and makes possible to use the information presented as an introduction to this area on the one hand, and to find more complicated publications of interest on the other hand.

For the case of subcooled surface boiling under forced convection the analytic expression of analogy between the heat transfer and carry pulse (Reynolds analogy) is derived. It is concluded that the obtained dependence creates the basis for solution of a series of problems of surface boiling physics. On the basis of the performed analysis the method of coordinate calculation of the origin of intensive vapour generation is developed and the formula for calculation of the broken-off-bubble radius under forced convection is derived [ru

Full Text Available The mixed convection flow past a horizontal plate being aligned through a small angle of attack to a uniform free stream will be considered in the limit of large Reynolds number and small Richardson number. Even a small angle of inclination of the wake is sufficient for the buoyancy force to accelerate the flow in the wake which causes a velocity overshoot in the wake. Moreover a hydrostatic pressure difference across the wake induces a correction to the potential flow which influences the inclination of the wake. Thus the wake and the correction of the potential flow have to be determined simultaneously. However, it turns out that solutions exist only if the angle of attack is sufficiently large. Solutions are computed numerically and the influence of the buoyancy on the lift coefficient is determined.

Full Text Available Portability and autonomy for biomedical diagnostic devices are two rising requirements. It is recognized that low-energy heating of such portable devices is of utmost importance for molecular recognition. This work focuses on screen-printed microheaters based on on Joule effect, which constitute an interesting solution for low-energy heating. An experimental study of the natural convection phenomena occurring with such microheaters is conducted. When they are suspended in the air, and because of the thinness of the supporting film, it is shown that the contributions of both the upward and downward faces have to be taken into account. A total Nusselt number and a total convective heat transfer coefficient have been used to describe the natural convection around these microheaters. In addition a relation between the Nusselt number and the Rayleigh number is derived, leading to an accurate prediction of the heating temperature (MRE< 2 %.

Thermoconvective instabilities in horizontal fluid layers are discussed with emphasis on the Rayleigh-Benard model problem. Steady solutions and time-dependent phenomena (relaxation oscillations and transition to turbulence) are studied within the nonlinear Boussinesq-Oberbeck approximation. Homogeneous steady solutions, limit cycles, and inhomogeneous (ordered) spatial structures are also studied in simple reaction-diffusion systems. Lastly, the non-periodic attractor that appears at large Rayleigh numbers in the truncated Boussinesq-Oberbeck model of Lorenz, is constructed, and a discussion of turbulent behavior is given. (author) [es

Early theoretical work on heat transfer in porous media focussed its attention on the onset of natural convection and cellular convection in rectangular enclosures with heating from below. Recently, increased attention has been directed to the study of natural convection in a porous medium external to heated surfaces and bodies. Boundary layer approximations were introduced, and similarly solutions have been obtained for steady natural convection boundary layers adjacent to a heated flat plate, a horizontal cylinder and a sphere as well as other two-dimensional and axisymmetric bodies of arbitrary shape. Higher order boundary layer theories have been carried out to assess the accuracy of the boundary layer approximation. The effects of entrainments at the edge of the boundary layer, the inclination angle of the heated inclined plate, and the upstream geometry on the heat transfer characteristics have been investigated based on the method of matched asymptotic expansions. The conditions for the onset of vortex instability in porous layers heated from below were determined based on linear stability analyses. The effects of no-slip boundary conditions, non-Darcy and thermal dispersion, which were neglected in all of the previous theoretical investigations, have recently been re-examined. Experimental investigations on natural convection about a vertical and inclined heated plate, a horizontal cylinder, as well as plume rise from a horizontal line source of heat have been conducted. All of this work is reviewed in this paper

Full Text Available The problem of mixed convection of a viscous incompressible fluid in an open rectangular reservoir with inlet and outlet of mass with considering nonuniform heat sink at the external borders of the solution domain is solved. The region of the solution was limited by two vertical and by one horizontal walls of finite thickness and one free surface. The flat nonstationary mixed convection within the framework of Navier-Stokes model is examined for liquid and thermal conductivity for solid walls. Distributions of hydrodynamic parameters and temperatures with different intensity of heat sink on the outer contour of the cavity show a change in the intensity of heat sink on the region boundaries of the solution leads to scale changes in the structure of flow and temperature fields of the liquids.

Thermal-convection-induced defects can cause huge loss in the power conversion efficiency of solution-processed perovskite solar cells. We investigated two types of convection in perovskite solution during the formation of perovskite films. By balancing the convection via special configurations of surface tension and boiling point in mixed γ-butyrolactone (GBL) and dimethylsulfoxide (DMSO), we removed microscopic defects such as rings, bumps, and crevices. The deposited perovskite films were smooth and dense, which enabled a high power conversion efficiency of 17.7% in a 1 cm2 cell area. We believe that the present strategy for controlling the convection can be helpful in improving the perovskite film quality for solvent-rich scalable solution processes of solar cells such as doctor blading, soft-cover deposition, printing, and slot-die coating.

The main objectives of this thesis are the direct numerical simulation of natural convection in a vertical differentially heated slot and the improvements of second-order turbulence modelling. A three-dimensional direct numerical simulation code has been developed in order to gain a better understanding of turbulence properties in natural convection flows. This code has been validated in several physical configurations: non-stratified natural convection flows (conduction solution), stratified natural convection flows (double boundary layer solution), transitional and turbulent Poiseuille flows. For the conduction solution, the turbulent regime was reached at a Rayleigh number of 1*10 5 and 5.4*10 5 . A detailed analysis of these results has revealed the principal qualities of the available models but has also pointed our their shortcomings. This data base has been used in order to improve the triple correlations transport models and to select the turbulent time scales suitable for such flows. (author). 122 refs., figs., tabs., 4 appends

Mantle convection is the cause for plate tectonics, the formation of mountains and oceans, and the main driving mechanism behind earthquakes. The convection process is modeled by a system of partial differential equations describing the conservation of mass, momentum and energy. Characteristic to mantle flow is the vast disparity of length scales from global to microscopic, turning mantle convection simulations into a challenging application for high-performance computing. As system size and technical complexity of the simulations continue to increase, design and implementation of simulation models for next generation large-scale architectures is handled successfully only in an interdisciplinary context. A new priority program - named SPPEXA - by the German Research Foundation (DFG) addresses this issue, and brings together computer scientists, mathematicians and application scientists around grand challenges in HPC. Here we report from the TERRA-NEO project, which is part of the high visibility SPPEXA program, and a joint effort of four research groups. TERRA-NEO develops algorithms for future HPC infrastructures, focusing on high computational efficiency and resilience in next generation mantle convection models. We present software that can resolve the Earth's mantle with up to 1012 grid points and scales efficiently to massively parallel hardware with more than 50,000 processors. We use our simulations to explore the dynamic regime of mantle convection and assess the impact of small scale processes on global mantle flow.

The nature and magnitude of the hazard from radioactivity posed by a possible nuclear accident depend strongly on convective behaviour within and immediately adjacent to the plant in question. This behaviour depends upon the nature of the vapour-gas-aerosol mixture concerned, and can show unusual properties such as 'upside-down' convection in which hot mixtures fall and cold mixtures rise. Predictions and criteria as to the types of behaviour which could possibly occur are summarised. Possible applications to present reactors are considered, and ways in which presently expected convection could be drastically modified are described. In some circumstances these could be used to suppress the radioactive source term or to switch its effect between distant dilute contamination and severe local contamination. (author). 8 refs, 2 figs, 2 tabs

In this paper a review of recent developments of turbulence models for natural convection in enclosures is presented. The emphasis is placed on the effect of the treatments of Reynolds stress and turbulent heat flux on the stability and accuracy of the solution for natural convection in enclosures. The turbulence models considered in the preset study are the two-layer k -ε model, the shear stress transport (SST) model, the elliptic-relaxation (V2-f) model and the elliptic-blending second-moment closure (EBM). Three different treatments of the turbulent heat flux are the generalized gradient diffusion hypothesis (GGDH), the algebraic flux model (AFM) and the differential flux model (DFM). The mathematical formulation of the above turbulence models and their solution method are presented. Evaluation of turbulence models are performed for turbulent natural convection in a 1:5 rectangular cavity ( Ra = 4.3x10 10 ) and in a square cavity with conducting top and bottom walls ( Ra =1.58x10 9 ) and the Rayleigh-Benard convection ( Ra = 2x10 6 ∼ Ra =10 9 ). The relative performances of turbulence models are examined and their successes and shortcomings are addressed

An investigation of forced convection heat transfer in He II is conducted. The study includes both experimental and theoretical treatments of the problem. The experiment consists of a hydraulic pump and a copper flow tube, 3 mm in ID and 2m long. The system allows measurements of one-dimensional heat and mass transfer in He II. The heat transfer experiments are performed by applying heat at the midpoint along the length of the flow tube. Two modes of heat input are employed, i.e., step function heat input and square pulse heat input. The heat transfer results are discussed in terms of temperature distribution in the tube. The experimental temperature profiles are compared with numerical solutions of an analytical model developed from the He II energy equation. The bath temperature is set at three different values of 1.65, 1.80, and 1.95 K. The He II flow velocity is varied up to 90 cm/s. Pressure is monitored at each end of the flow tube, and the He II pressure drop is obtained for different flow velocities. Results indicate that He II heat transfer by forced convention is considerably higher than that by internal convection. The theoretical model is in close agreement with the experiment. He II pressure drop and friction factor are very similar to those of an ordinary fluid

Macro voids are undesirable large pores in membranes used for purification. They form when membranes are cast as thin films on a smooth surface by evaporating solvent (acetone) from a polymer solution. There are two un-tested hypotheses explaining the growth of macro voids. One states that diffusion of the non-solvent (water) is solely responsible, while the other states that solutocapillary convection is the primary cause of macro void growth. Solutocapillary convection is flow-caused by a concentration induced surface-tension gradient. Macrovoid growth in the former hypothesis is gravity independent, while in the latter it is opposed by gravity. To distinguish between these two hypotheses, experiments were designed to cast membranes in zero-gravity. A semi-automated apparatus was designed and built for casting membranes during the 20 secs of zero-g time available in parabolic aircraft flight such as NASA's KC-135. The phase changes were monitored optically, and membrane morphology was evaluated by scanning electron microscopy (SEM). These studies appear to be the first quantitative studies of membrane casting in micro-gravity which incorporate real-time data acquisition. Morphological studies of membranes cast at 0, 1, and 1.8 g revealed the presence of numerous, sparse and no macrovoids respectively. These results are consistent with the predictions of the solutocapillary hypothesis of macrovoid growth.

The effective diffusion coefficient D* of a passive component, such as test particles, dye, temperature, magnetic flux, etc., is derived for motion in periodic two-dimensional incompressible convective flow with characteristic velocity v and size d in the presence of an intrinsic local diffusivity D. Asymptotic solutions for effective diffusivity D*(P) in the large P limit, with P ∼ vd/D, is shown to be of the form D* = cDP/sup 1/2/ with c being a coefficient that is determined analytically. The constant c depends on the geometry of the convective cell and on an average of the flow speed along the separatrix. The asymptotic method of evaluation applies to both free boundary and rough boundary flow patterns and it is shown that the method can be extended to more complicated patterns such as the flows generated by rotating cylinders, as in the problem considered by Nadim, Cox, and Brenner [J. Fluid Mech., 164: 185 (1986)]. The diffusivity D* is readily calculated for small P, but the evaluation for arbitrary P requires numerical methods. Monte Carlo particle simulation codes are used to evaluate D* at arbitrary P, and thereby describe the transition for D* between the large and small P limits

This report deals with the topology optimization of convection problems.That is, the aim of the project is to develop, implement and examine topology optimization of purely thermal and coupled thermomechanical problems,when the design-dependent eects of convection are taken into consideration.......This is done by the use of a self-programmed FORTRAN-code, which builds on an existing 2D-plane thermomechanical nite element code implementing during the course `41525 FEM-Heavy'. The topology optimizationfeatures have been implemented from scratch, and allows the program to optimize elastostatic mechanical...

Some common experimental techniques to determine local velocities and to visualize temperature fields in natural convection research are discussed. First the physics and practice of anemometers are discussed with emphasis put on optical anemometers. In the second and third case the physics and practice of the most developed interferometers are discussed; namely differential interferometry for visualization of temperature gradient fields and holographic interferometry for visualization of temperature fields. At the Institut fuer Reaktorbauelemente these three measuring techniques are applied for convection and pipe flow studies. (orig.) [de

Three-dimensional, time-dependent convection in a plane layer of fluid, uniformly heated from below and subject to vertical shear and to rotation about an axis tilted from the vertical, was simulated by the numerical solution of the Boussinesq equations, including all Coriolis terms. Rotation about a vertical axis produces smaller convection cells with diminished heat fluxes and considerable vorticity. When the rotation axis is tilted from the vertical to represent tropical latitudes, the convection cells become elongated in a N-S direction. Imposed flows with constant vertical shear produce convective rolls aligned with the mean flow. When the rotation vector is tilted from the vertical, the competing effects due to rotation and shear can stabilize the convective motions. 15 references

A new statistical modeling technique for determining the global ionospheric convection is described. The principal component regression (PCR)-based technique is based on Super Dual Auroral Radar Network (SuperDARN) observations and is an advanced version of the PCR technique that Waters et al. (https//:doi.org.10.1002/2015JA021596) used for the SuperMAG data. While SuperMAG ground magnetic field perturbations are vector measurements, SuperDARN provides line-of-sight measurements of the ionospheric convection flow. Each line-of-sight flow has a known azimuth (or direction), which must be converted into the actual vector flow. However, the component perpendicular to the azimuth direction is unknown. Our method uses historical data from the SuperDARN database and PCR to determine a fill-in model convection distribution for any given universal time. The fill-in data process is driven by a list of state descriptors (magnetic indices and the solar zenith angle). The final solution is then derived from a spherical cap harmonic fit to the SuperDARN measurements and the fill-in model. When compared with the standard SuperDARN fill-in model, we find that our fill-in model provides improved solutions, and the final solutions are in better agreement with the SuperDARN measurements. Our solutions are far less dynamic than the standard SuperDARN solutions, which we interpret as being due to a lack of magnetosphere-ionosphere inertia and communication delays in the standard SuperDARN technique while it is inherently included in our approach. Rather, we argue that the magnetosphere-ionosphere system has inertia that prevents the global convection from changing abruptly in response to an interplanetary magnetic field change.

Observations suggest that the large-scale convective velocities obtained by solar convection simulations might be over-estimated (convective conundrum). One plausible solution to this could be the small-scale dynamo which cannot be fully resolved by global simulations. The small-scale Lorentz force suppresses the convective motions and also the turbulent mixing of entropy between upflows and downflows, leading to a large effective Prandtl number (Pr). We explore this idea in three-dimensional global rotating convection simulations at different thermal conductivity (κ), i.e., at different Pr. In agreement with previous non-rotating simulations, the convective velocity is reduced with the increase of Pr as long as the thermal conductive flux is negligible. A subadiabatic layer is formed near the base of the convection zone due to continuous deposition of low entropy plumes in low-κ simulations. The most interesting result of our low-κ simulations is that the convective motions are accompanied by a change in the convection structure that is increasingly influenced by small-scale plumes. These plumes tend to transport angular momentum radially inward and thus establish an anti-solar differential rotation, in striking contrast to the solar rotation profile. If such low diffusive plumes, driven by the radiative-surface cooling, are present in the Sun, then our results cast doubt on the idea that a high effective Pr may be a viable solution to the solar convective conundrum. Our study also emphasizes that any resolution of the conundrum that relies on the downward plumes must take into account the angular momentum transport and heat transport.

In this decade, a new technique for the study of ionosphere electrodynamics has been implemented in an evolving generation of high-latitude HF radars. Coherent backscatter from electron density irregularities at F region altitudes is utilized to observe convective plasma motion. The electronic beam forming and scanning capabilities of the radars afford an excellent combination of spatial (∼50 km) and temporal (∼1 min) resolution of the large-scale (∼10 6 km 2 ) convection pattern. In this paper, we outline the methods developed to synthesize the HF radar data into two-dimensional maps of convection velocity. Although any single radar can directly measure only the line-of-sight, or radial, component of the plasma motion, the convection pattern is sometimes so uniform and stable that scanning in azimuth serves to determine the transverse component as well. Under more variable conditions, data from a second radar are necessary to unambiguously resolve velocity vectors. In either case, a limited region of vector solution can be expanded into contiguous areas of single-radar radial velocity data by noting that the convection must everywhere be divergence-free, i.e., ∇·v=0. It is thus often possible to map velocity vectors without extensive second-radar coverage. We present several examples of two-dimensional velocity maps. These show instances of L shell-aligned flow in the dusk sector, the reversal of convection near magnetic midnight, and counterstreaming in the dayside cleft. We include a study of merged coherent and incoherent radar data that illustrates the applicability of these methods to other ionospheric radar systems. copyright American Geophysical Union 1989

The development of convective boiling heat transfer correlations and analytical models has almost exclusively been based on measurements of the total heat flux, and therefore on the overall two-phase heat transfer coefficient, when the well-known heat transfer correlations have often assumed additive mechanisms, one for each mode of heat transfer, convection and boiling. While the global performance of such correlations can readily be assessed, the predictive capability of the individual components of the correlation has usually remained elusive. This becomes important when, for example, developing mechanistic models for subcooled void formation based on the partitioning of the wall heat flux into a boiling and a convective component, or when extending a correlation beyond its original range of applications where the preponderance of the heat transfer mechanisms involved can be significantly different. A new examination of existing experimental heat transfer data obtained under fixed hydrodynamic conditions, whereby the local flow conditions are decoupled from the local heat flux, has allowed the unequivocal isolation of the boiling contribution over a broad range of thermodynamic qualities (0 to 0.8) for water at 7 MPa. Boiling suppression, as the quality increases, has consequently been quantified, thus providing valuable new insights on the functionality and contribution of boiling in convective flows. (author)

In this article, natural convection in a square porous enclosure is simulated by a direct numerical method. The solution method is based on a random distribution of solid blocks, which resembles the porous media within the cavity. The Navier-Stokes equations are solved directly in the fluid region without the assumption of volume averaging. The no-slip condition is applied on the surface of any solid particle, and the energy transport equation is solved separately for the solid phase and fluid flow. The local and average Nusselt numbers are presented for steady state for two different cases of thermal boundary conditions of the cavity walls. An oscillatory solution is observed for the local Nu number on the surface of the enclosure, and the critical Ra numbers are found in which natural convection flow is started within the cavity

In this paper, we study the asymptotic behaviour of the solution of a convective heat transfer boundary problem in an ɛ -periodic domain which consists of two interwoven phases, solid and fluid, separated by an interface. The fluid flow and its dependence with respect to the temperature are governed by the Boussinesq approximation of the Stokes equations. The tensors of thermal diffusion of both phases are ɛ -periodic, as well as the heat transfer coefficient which is used to describe the first-order jump condition on the interface. We find by homogenization that the two-scale limits of the solutions verify the most common system used to describe local thermal non-equilibrium phenomena in porous media (see Nield and Bejan in Convection in porous media, Springer, New York, 1999; Rees and Pop in Transport phenomena in porous media III, Elsevier, Oxford, 2005). Since now, this system was justified only by volume averaging arguments.

Laminar Flow and Convective Transport Processes: Scaling Principles and Asymptotic Analysis presents analytic methods for the solution of fluid mechanics and convective transport processes, all in the laminar flow regime. This book brings together the results of almost 30 years of research on the use of nondimensionalization, scaling principles, and asymptotic analysis into a comprehensive form suitable for presentation in a core graduate-level course on fluid mechanics and the convective transport of heat. A considerable amount of material on viscous-dominated flows is covered.A unique feat

We have studied turbulent convection in a vertical thin (Hele-Shaw) cell at very high Rayleigh numbers (up to 7x10 4 times the value for convective onset) through experiment, simulation, and analysis. Experimentally, convection is driven by an imposed concentration gradient in an isothermal cell. Model equations treat the fields in two dimensions, with the reduced dimension exerting its influence through a linear wall friction. Linear stability analysis of these equations demonstrates that as the thickness of the cell tends to zero, the critical Rayleigh number and wave number for convective onset do not depend on the velocity conditions at the top and bottom boundaries (i.e., no-slip or stress-free). At finite cell thickness δ, however, solutions with different boundary conditions behave differently. We simulate the model equations numerically for both types of boundary conditions. Time sequences of the full concentration fields from experiment and simulation display a large number of solutal plumes that are born in thin concentration boundary layers, merge to form vertical channels, and sometimes split at their tips via a Rayleigh-Taylor instability. Power spectra of the concentration field reveal scaling regions with slopes that depend on the Rayleigh number. We examine the scaling of nondimensional heat flux (the Nusselt number, Nu) and rms vertical velocity (the Pacute eclet number, Pe) with the Rayleigh number (Ra * ) for the simulations. Both no-slip and stress-free solutions exhibit the scaling NuRa * ∼Pe 2 that we develop from simple arguments involving dynamics in the interior, away from cell boundaries. In addition, for stress-free solutions a second relation, Nu∼√(nPe), is dictated by stagnation-point flows occurring at the horizontal boundaries; n is the number of plumes per unit length. (Abstract Truncated)

Effects of non-uniform heating in the core and additional forced circulation during decay heat removal operation are studied with a simplified mixed convection loop. The heat transfer coefficient is calculated analytically and measured experimentally. The analytic solution obtained from a one-dimensional heat equation is found to agree well with the experimental results. The effects of the non-uniform heating and the forced circulation are discussed

A method is introduced for diagnosing a transilient matrix for moist convection. This transilient matrix quantifies the nonlocal transport of air by convective eddies: for every height z, it gives the distribution of starting heights z{prime} for the eddies that arrive at z. In a cloud-resolving simulation of deep convection, the transilient matrix shows that two-thirds of the subcloud air convecting into the free troposphere originates from within 100 m of the surface. This finding clarifies which initial height to use when calculating convective available potential energy from soundings of the tropical troposphere.

Context: In spite of all the advances in multi-dimensional hydrodynamics, investigations of stellar evolution and stellar pulsations still depend on one-dimensional computations. This paper devises an alternative to the mixing-length theory or turbulence models usually adopted in modelling convective transport in such studies. Aims: The present work attempts to develop a time-dependent description of convection, which reflects the essential physics of convection and that is only moderately dependent on numerical parameters and far less time consuming than existing multi-dimensional hydrodynamics computations. Methods: Assuming that the most extensive convective patterns generate the majority of convective transport, the convective velocity field is described using two parallel, radial columns to represent up- and downstream flows. Horizontal exchange, in the form of fluid flow and radiation, over their connecting interface couples the two columns and allows a simple circulating motion. The main parameters of this convective description have straightforward geometrical meanings, namely the diameter of the columns (corresponding to the size of the convective cells) and the ratio of the cross-section between up- and downdrafts. For this geometrical setup, the time-dependent solution of the equations of radiation hydrodynamics is computed from an implicit scheme that has the advantage of being unaffected by the Courant-Friedrichs-Lewy time-step limit. This implementation is part of the TAPIR-Code (short for The adaptive, implicit RHD-Code). Results: To demonstrate the approach, results for convection zones in Cepheids are presented. The convective energy transport and convective velocities agree with expectations for Cepheids and the scheme reproduces both the kinetic energy flux and convective overshoot. A study of the parameter influence shows that the type of solution derived for these stars is in fact fairly robust with respect to the constitutive numerical

To investigate the real-world relevance of idealized-model convective self-aggregation, five 15 day cases of real organized convection in the tropics are simulated. These include multiple simulations of each case to test sensitivities of the convective organization and mean states to interactive radiation, interactive surface fluxes, and evaporation of rain. These simulations are compared to self-aggregation seen in the same model configured to run in idealized radiative-convective equilibrium. Analysis of the budget of the spatial variance of column-integrated frozen moist static energy shows that control runs have significant positive contributions to organization from radiation and negative contributions from surface fluxes and transport, similar to idealized runs once they become aggregated. Despite identical lateral boundary conditions for all experiments in each case, systematic differences in mean column water vapor (CWV), CWV distribution shape, and CWV autocorrelation length scale are found between the different sensitivity runs, particularly for those without interactive radiation, showing that there are at least some similarities in sensitivities to these feedbacks in both idealized and realistic simulations (although the organization of precipitation shows less sensitivity to interactive radiation). The magnitudes and signs of these systematic differences are consistent with a rough equilibrium between (1) equalization due to advection from the lateral boundaries and (2) disaggregation due to the absence of interactive radiation, implying disaggregation rates comparable to those in idealized runs with aggregated initial conditions and noninteractive radiation. This points to a plausible similarity in the way that radiation feedbacks maintain aggregated convection in both idealized simulations and the real world.Plain Language SummaryUnderstanding the processes that lead to the organization of tropical rainstorms is an important challenge for weather

The CRUCIB code was written in support of an experimental program aimed at measurement of thermal diffusivities of refractory liquids. Precise values of diffusivity are necessary to realistic analysis of reactor safety problems, nuclear waste disposal procedures, and fundamental metal forming processes. The code calculates the axisymmetric transient convective motions produced in a right circular cylindrical crucible, which is surface heated by an annular heat pulse. Emphasis of this report is placed on the input-output options of the CRUCIB code, which are tailored to assess the importance of the convective heat transfer in determining the surface temperature distribution. Use is limited to Prandtl numbers less than unity; larger values can be accommodated by replacement of a single block of the code, if desired. (U.S.)

Complexity—nonlinear dynamics for my purposes in this essay—is rich with metaphysical and epistemological implications but is receiving sustained philosophical analysis only recently. I will explore some of the subtleties of causation and constraint in Rayleigh–Bénard convection as an example of a complex phenomenon, and extract some lessons for further philosophical reflection on top-down constraint and causation particularly with respect to causal foundationalism. PMID:23386955

This is a report prepared by a group interested in doing research in thermal convection using the large scale refrigeration facilities available at the SSC Laboratories (SSCL). The group preparing this report consists of Michael McAshan at SSCL, Robert Behringer at Duke University, Katepalli Sreenivasan at Yale University, Xiao-Zhong Wu at Northern Illinois University and Russell Donnelly at the University of Oregon, who served as Editor for this report. This study reports the research and development opportunities in such a project, the technical requirements and feasibility of its construction and operation, and the costs associated with the needed facilities and support activities. The facility will be a unique national resource for studies of high-Reynolds-number and high-Rayleigh-number and high Rayleigh number turbulence phenomena, and is one of the six items determined as suitable for potential funding through a screening of Expressions of Interest. The proposed facility is possible only because of the advanced cryogenic technology available at the SSCL. Typical scientific issues to be addressed in the facility will be discussed. It devolved during our study, that while the main experiment is still considered to be the thermal convection experiment discussed in our original Expression of Interest, there are now a very substantial set of other, important and fundamental experiments which can be done with the large cryostat proposed for the convection experiment. We believe the facility could provide several decades of front-line research in turbulence, and shall describe why this is so

This paper presents a mathematical model for directional solidification of a binary alloy including a dendritic region underlying an all-liquid region. It is assumed initially that there exists a nonconvecting state with planar isotherms and isoconcentrates solidifying at a constant velocity. The stability of this system has been analyzed and nonlinear calculations are performed that show the effect of convection in the solidification process when the system is unstable. Results of calculations for various cases defined by the initial temperature gradient at the dendrite tips and varying strength of the gravitational field are presented for systems involving lead-tin alloys. The results show that the systems are stable for a gravitational constant of 0.0001 g(0) and that convection can be suppressed by appropriate choice of the container's size for higher values of the gravitational constant. It is also concluded that for the lead-tin systems considered, convection in the mushy zone is not significant below the upper 20 percent of the dendritic zone, if al all.

A linear theory is presented of the current convective instability in the long wavelength limit, i.e., kL >ω) and inertial (ν/sub i/n>>ω) limits where ω is the wave frequency and ν/sub i/n is the ion-neutral collision frequency. It is shown that the growth rate scales as k in the collisional limit and as k/sup 2/3/ in the inertial limit. The analytical solutions are compared to exact numerical solutions, and very good agreement is found. Applications to the auroral ionosphere are discussed

In this paper we study mathematically an industrial problem related to sterilization processes involving heat transfer by natural convection. We give results of existence and regularity for the solution of this problem. We recast the whole problem as an optimal control problem with pointwise constraints on the state and the control in order to ensure the reduction of microorganism concentration and the retention of nutrients, and to save energy. Finally, we give results on existence of the optimal solution and optimality conditions for its characterization.

In the past various arguments have been used for applying kinetic energy-conserving advection schemes in numerical simulations of incompressible fluid flows. One argument is obeying the programmed dissipation by viscous stresses or by sub-grid stresses in Direct Numerical Simulation and Large Eddy Simulation, see e.g. [Phys. Fluids A 3 (7) (1991) 1766]. Another argument is that, according to e.g. [J. Comput. Phys. 6 (1970) 392; 1 (1966) 119], energy-conserving convection schemes are more stable i.e. by prohibiting a spurious blow-up of volume-integrated energy in a closed volume without external energy sources. In the above-mentioned references it is stated that nonlinear instability is due to spatial truncation rather than to time truncation and therefore these papers are mainly concerned with the spatial integration. In this paper we demonstrate that discretized temporal integration of a spatially variance-conserving convection scheme can induce non-energy conserving solutions. In this paper the conservation of the variance of a scalar property is taken as a simple model for the conservation of kinetic energy. In addition, the derivation and testing of a variance-conserving scheme allows for a clear definition of kinetic energy-conserving advection schemes for solving the Navier-Stokes equations. Consequently, we first derive and test a strictly variance-conserving space-time discretization for the convection term in the convection-diffusion equation. Our starting point is the variance-conserving spatial discretization of the convection operator presented by Piacsek and Williams [J. Comput. Phys. 6 (1970) 392]. In terms of its conservation properties, our variance-conserving scheme is compared to other spatially variance-conserving schemes as well as with the non-variance-conserving schemes applied in our shallow-water solver, see e.g. [Direct and Large-eddy Simulation Workshop IV, ERCOFTAC Series, Kluwer Academic Publishers, 2001, pp. 409-287

This study investigates a variety of features present in a new configuration of the Community Atmosphere Model (CAM) variant, SP-CAM 2.0. The new configuration (multiple-parameterization-CAM, MP-CAM) changes the manner in which the super-parameterization (SP) concept represents physical tendency feedbacks to the large-scale by using the mean of 10 independent two-dimensional cloud-permitting model (CPM) curtains in each global model column instead of the conventional single CPM curtain. The climates of the SP and MP configurations are examined to investigate any significant differences caused by the application of convective physical tendencies that are more deterministic in nature, paying particular attention to extreme precipitation events and large-scale weather systems, such as the Madden-Julian Oscillation (MJO). A number of small but significant changes in the mean state climate are uncovered, and it is found that the new formulation degrades MJO performance. Despite these deficiencies, the ensemble of possible realizations of convective states in the MP configuration allows for analysis of uncertainty in the small-scale solution, lending to examination of those weather regimes and physical mechanisms associated with strong, chaotic convection. Methods of quantifying precipitation predictability are explored, and use of the most reliable of these leads to the conclusion that poor precipitation predictability is most directly related to the proximity of the global climate model column state to atmospheric critical points. Secondarily, the predictability is tied to the availability of potential convective energy, the presence of mesoscale convective organization on the CPM grid, and the directive power of the large-scale.

For convection-dominated flows, classical second-order methods are notoriously oscillatory and often unstable. For this reason, many computational fluid dynamicists have adopted various forms of (inherently stable) first-order upwinding over the past few decades. Although it is now well known that first-order convection schemes suffer from serious inaccuracies attributable to artificial viscosity or numerical diffusion under high convection conditions, these methods continue to enjoy widespread popularity for numerical heat transfer calculations, apparently due to a perceived lack of viable high accuracy alternatives. But alternatives are available. For example, nonoscillatory methods used in gasdynamics, including currently popular TVD schemes, can be easily adapted to multidimensional incompressible flow and convective transport. This, in itself, would be a major advance for numerical convective heat transfer, for example. But, as is shown, second-order TVD schemes form only a small, overly restrictive, subclass of a much more universal, and extremely simple, nonoscillatory flux-limiting strategy which can be applied to convection schemes of arbitrarily high order accuracy, while requiring only a simple tridiagonal ADI line-solver, as used in the majority of general purpose iterative codes for incompressible flow and numerical heat transfer. The new universal limiter and associated solution procedures form the so-called ULTRA-SHARP alternative for high resolution nonoscillatory multidimensional steady state high speed convective modelling.

Several improvements are implemented in the Zhang-McFarlane (ZM) convection scheme to investigate the roles of convection parameterization in the formation of double intertropical convergence zone (ITCZ) bias in the NCAR CESM1.2.1. It is shown that the prominent double ITCZ biases of precipitation, sea surface temperature (SST), and wind stress in the standard CESM1.2.1 are largely eliminated in all seasons with the use of these improvements in convection scheme. This study for the first time demonstrates that the modifications of convection scheme can eliminate the double ITCZ biases in all seasons, including boreal winter and spring. Further analysis shows that the elimination of the double ITCZ bias is achieved not by improving other possible contributors, such as stratus cloud bias off the west coast of South America and cloud/radiation biases over the Southern Ocean, but by modifying the convection scheme itself. This study demonstrates that convection scheme is the primary contributor to the double ITCZ bias in the CESM1.2.1, and provides a possible solution to the long-standing double ITCZ problem. The atmospheric model simulations forced by observed SST show that the original ZM convection scheme tends to produce double ITCZ bias in high SST scenario, while the modified convection scheme does not. The impact of changes in each core component of convection scheme on the double ITCZ bias in atmospheric model is identified and further investigated.

At the base of the solar convection zone lies the solar tachocline. This internal interface is where motions from the unstable convection zone above overshoot and penetrate downward into the stiffly stable radiative zone below, driving gravity waves, mixing, and possibly pumping and storing magnetic fields. Here we study the dynamics of convective overshoot across very stiff interfaces with some properties similar to the internal boundary layer within the Sun. We use the Dedalus pseudospectral framework and study fully compressible dynamics at moderate to high Peclet number and low Mach number, probing a regime where turbulent transport is important, and where the compressible dynamics are similar to those of convective motions in the deep solar interior. We find that the depth of convective overshoot is well described by a simple buoyancy equilibration model, and we consider implications for dynamics at the solar tachocline and for the storage of magnetic fields there by overshooting convection.

Dynamics Explorer 2 (DE 2) electric field and ion drift data are used in a statistical study of the ionospheric convection electric field in bulge-type auroral substorms. Thirty-one individual DE 2 substorm crossings were carefully selected and organized by the use of global auroral images obtained...... this database enabled us to compile a model of the ionospheric convection electric field. The characteristics of the premidnight convection reversal show a pronounced local time dependency. Far west of the surge it is a fairly well defined point reversal or convection shear. Approaching the surge and within...... the surge it is a region of weak electric fields increasing in width toward midnight that separates regions of equatorward and poleward electric fields. Therefore we adopt the term Harang region rather than the Harang discontinuity for the premidnight convection reversal. A relatively narrow convection...

The structure of solar magnetic fields is dominated by the effects of convection, which should be incorporated in any model of the solar cycle. Although mixing length theory is adequate for calculating the structure of main sequence stars, a better description of convection is needed for any detailed dynamo model. Recent work on nonlinear convection at low Prandt numbers is reviewed. There has been some progress towards a theory of compressible convection, though there is still no firm theoretical evidence for cells with scales less than the depth of the convecting layer. However, it remains likely that the pattern of solar convection is dominated by granules, supergranules and giant cells. The effects of rotation on these cells are briefly considered. (Auth.)

The nonlinear spatiotemporal evolution of convective flows is numerically investigated in the case of colloidal suspension filling an inclined closed cell heated from below. The bifurcation diagram (the dependency of the Nusselt number on the Rayleigh number) is obtained. The characteristics of the wave and steady patterns are investigated depending on heat intensity. The travelling wave changing travel direction and the non-regular oscillatory flow are found to be stable solutions within a certain interval of the Rayleigh number. Temporal Fourier decomposition is used together with other diagnostic tools to analyse the complex bifurcation and spatiotemporal properties caused by the interplay of the gravity-induced gradient of concentration and convective mixing of the fluid. It is shown that a more complex flow structure exists at a lower heating intensity (Rayleigh number). (paper)

This paper presents a theoretical and computational investigation of convection, diffusion, and adsorption in surface-based biosensors. In particular, we study the transport dynamics in a model geometry of a surface plasmon resonance (SPR) sensor. The work, however, is equally relevant for other...... microfluidic surface-based biosensors, operating under flow conditions. A widely adopted approximate quasi-steady theory to capture convective and diffusive mass transport is reviewed, and an analytical solution is presented. An expression of the Damköhler number is derived in terms of the nondimensional...... concentration to the maximum surface capacity is critical for reliable use of the quasi-steady theory. Finally, our results provide users of surface-based biosensors with a tool for correcting experimentally obtained adsorption rate constants....

The influences of feedback control and internal heat source on the onset of Rayleigh-Bénard convection in a horizontal nanofluid layer is studied analytically due to Soret and Dufour parameters. The confining boundaries of the nanofluid layer (bottom boundary-top boundary) are assumed to be free-free, rigid-free, and rigid-rigid, with a source of heat from below. Linear stability theory is applied, and the eigenvalue solution is obtained numerically using the Galerkin technique. Focusing on the stationary convection, it is shown that there is a positive thermal resistance in the presence of feedback control on the onset of double-diffusive convection, while there is a positive thermal efficiency in the existence of internal heat generation. The possibilities of suppress or augment of the Rayleigh-Bénard convection in a nanofluid layer are also discussed in detail.

Full Text Available In the present study, the influence of natural convection on the lamellar eutectic growth is determined by a phase-field-lattice Boltzmann study for Al-Cu eutectic alloy. The mass difference resulting from concentration difference led to the fluid flow, and a robust parallel and adaptive mesh refinement algorithm was employed to improve the computational efficiency without any compromising accuracy. Results show that the existence of natural convection would affect the growth undercooling and thus control the interface shape by adjusting the lamellar width. In particular, by alternating the magnitude of the solute expansion coefficient, the strength of the natural convection is changed. Corresponding microstructure patterns are discussed and compared with those under no-convection conditions.

Cylindrical Al-7 wt% Silicon, Al-19 wt% Copper and Lead-6 wt% Antimony alloy samples were directionally solidified (DS) with liquid above, solid below, and gravity pointing down, in graphite crucibles having an abrupt cross-sectional increase. These alloys have similar solidification shrinkage but are expected to have different degrees of thermosolutal convection during solidification. Microstructures in the DS samples in the vicinity of the section change have been studied in order to examine the effect of convection associated with the combined influence of thermosolutal effects and solidification shrinkage. Extensive radial and axial macrosegregation associated with cross-section change is observed. It also appears that steepling and local primary alpha-phase remelting resulting from convection are responsible for stray grain formation at the reentrant corners. Preliminary results from a numerical model, which includes solidification shrinkage and thermosolutal convection in the mushy zone, indicate that these regions are prone to solutal remelting of dendrites.

National Aeronautics and Space Administration — This innovative research effort is directed at determining, quantitatively, the convective heat transfer coefficients applicable to a Montgolfiere balloon operating...

Full Text Available We describe the large-scale model geodynamo, which based on indirect data of inhomogeneities in the density of the Earth’s core. Convection structure is associated with spherical harmonic Y24 , which defines the basic poloidal component of velocity. Coriolis drift of this mode determines the toroidal component of velocity. Thus, 6 convective cells are formed. The model takes into account the feedback effect of the magnetic field on convection. It was ascertained that the model contains stable regimes of field generation. The velocity of convection and the dipole component of the magnetic field are close to the observed ones.

outer core. Translation is a particular solution of Navier-Stokes equation with permeable boundary conditions, but depending on the viscosity of the solid core, modes with higher spherical harmonics degree can develop. At low viscosity, these modes can be dominant and dissipate the degree l=1 of thermal heterogeneities. Hence, a viscosity threshold may be expected below which translation cannot take place, thereby constraining the viscosity of iron at inner core conditions. Using a hybrid finite-difference spherical harmonics Navier-Stokes solver, we investigate the interplay between translation and convection in a 3D spherical model with permeable boundary conditions. Our numerical simulations show the dominance of pure translation for viscosities of the inner core higher than 5 x 1018 Pas. Translation is almost completely hampered by convective motions for viscosities lower than 1017 Pas and the phase change becomes an almost impermeable boundary. Between these values, a well developed circulation at the harmonic degree l=1 persists, but composed of localized cold downwellings, a passive upward flow taking place on the opposite side (the melting side). Such a convective structure remains compatible with the seismic asymmetry. Alboussiere, T., Deguen, R., Melzani, M., 2010. Nature 466 (7307), 744-U9. Monnereau, M., Calvet, M., Margerin, L., Souriau, A., 2010. Science 328 (5981), 1014-1017.

Full Text Available The size distribution of cumulus clouds due to shallow and deep convection is analyzed using satellite pictures, LES model results and data from the German rain radar network. The size distributions found can be described by simple power laws as has also been proposed for other cloud data in the literature. As the observed precipitation at ground stations is finally determined by cloud numbers in an area and individual sizes and rain rates of single clouds, the cloud size distributions might be used for developing empirical precipitation forecasts or for validating results from cloud resolving models being introduced to routine weather forecasts.

We perform 3D radiative hydrodynamic simulations to study the properties of convection in the superadiabatic layer of stars. The simulations show differences in both the stratification and turbulent quantities for different types of stars. We extract turbulent pressure and eddy sizes, as well as the T-τ relation for different stars and find that they are sensitive to the energy flux and gravity. We also show that contrary to what is usually assumed in the field of stellar atmospheres, the structure and gas dynamics of simulations of turbulent atmospheres cannot be parameterized with T eff and log(g) alone.

This paper presents an industrial application of topology optimization for combined conductive and convective heat transfer problems. The solution is based on a synergy of computer aided design and engineering software tools from Dassault Systemes. The considered physical problem of steady......-state heat transfer under convection is simulated using SIMULIA-Abaqus. A corresponding topology optimization feature is provided by SIMULIA-Tosca. By following a standard workflow of design optimization, the proposed solution is able to accommodate practical design scenarios and results in efficient...

We present an overview of the most relevant, and sometimes contrasting, theoretical approaches to Rayleigh-Taylor and mean-gradient-forced Rayleigh-Bénard two-dimensional turbulence together with numerical and experimental evidences for their support. The main aim of this overview is to emphasize that, despite the different character of these two systems, especially in relation to their steadiness/unsteadiness, turbulent fluctuations are well described by the same scaling relationships originated from the Bolgiano balance. The latter states that inertial terms and buoyancy terms balance at small scales giving rise to an inverse kinetic energy cascade. The main difference with respect to the inverse energy cascade in hydrodynamic turbulence [R. H. Kraichnan, "Inertial ranges in two-dimensional turbulence," Phys. Fluids 10, 1417 (1967)] is that the rate of cascade of kinetic energy here is not constant along the inertial range of scales. Thanks to the absence of physical boundaries, the two systems here investigated turned out to be a natural physical realization of the Kraichnan scaling regime hitherto associated with the elusive "ultimate state of thermal convection" [R. H. Kraichnan, "Turbulent thermal convection at arbitrary Prandtl number," Phys. Fluids 5, 1374-1389 (1962)].

The onset of double-diffusive convection in a couple-stress fluid-saturated horizontal porous layer is studied using linear and weak nonlinear stability analyses. The modified Darcy equation that includes the time derivative term and the inertia term is used to model the momentum equation. The expressions for stationary, oscillatory and finite-amplitude Rayleigh number are obtained as a function of the governing parameters. The effect of couple-stress parameter, solute Rayleigh number, Vadasz number and diffusivity ratio on stationary, oscillatory and finite-amplitude convection is shown graphically. It is found that the couple-stress parameter and the solute Rayleigh number have a stabilizing effect on stationary, oscillatory and finite-amplitude convection. The diffusivity ratio has a destabilizing effect in the case of stationary and finite-amplitude modes, with a dual effect in the case of oscillatory convection. The Vadasz number advances the onset of oscillatory convection. The heat and mass transfer decreases with an increase in the values of couple-stress parameter and diffusivity ratio, while both increase with an increase in the value of the solute Rayleigh number.

the characteristic size of moment of inertia anomalies decreases with higher Ra, but that the characteristic response time for TPW also decreases. These two effects approximately cancel. However, the orientation of the principal axes of the moment of inertia becomes less stable to perturbations at high Ra, thereby increasing the rate of TPW. Overall, I find that a more vigorously convecting planet is more likely to experience large TPW events. If early Earth had more vigorous convection, it may have experienced more TPW than present-day Earth. Flow induced by density anomalies in the mantle deflects free surfaces at the surface and the CMB, and the mass anomalies due to these deflections contribute to the moment of inertia. A full accounting of the moment of inertia anomalies must include these surface effects. Numerical models of mantle convection with a free surface have suffered from numerical sloshing instabilities. I analyze the sloshing instability by constructing a generalized eigenvalue problem for the relaxation time spectrum. The minimum relaxation time of the spectrum sets the maximum stable timestep. This analysis gives the first quantitative explanation for why existing techniques for stabilizing geodynamic simulations with a free surface work. I also use this perspective to construct an alternative stabilization scheme based on nonstandard finite differences. This scheme has a single parameter, given by an estimate of the minimum relaxation time, and allows for still larger timesteps. Finally, I develop a new method for analyzing apparent polar wander (APW) paths described by sequences of paleomagnetic poles. Existing techniques, such as spline fits and running means, do not fully account for the uncertainties in the position and timing of paleomagnetic pole paths. Furthermore, they impose regularization on the solution, and the resulting uncertainties are difficult to interpret. Our technique is an extension of paleomagnetic Euler pole (PEP) analysis. I

The article contains two parts. In the first part a condensed review of the most striking phenomena in Benard convection in laterally confined fluid layers is given. In the second part recent experimental and theoretical work on Benard convection in gaps is presented an analysed. (orig.) [de

The evolution of convection zones in cooling white dwarfs with helium envelopes and outer hydrogen layers is calculated with a complete stellar evolution code. It is shown that white dwarfs of spectral type DB cannot be formed from DA stars by convective mixing. However, for cooler temperatures (Tsub(e) [de

We show that Southern Ocean (SO) temperatures in the latest generation of Earth System Models exhibit two major modes of variation, one driven by deep convection, the other by tropical variability. We perform a CMIP5 model intercomparison to understand why different climate models represent SO variability so differently in long, control simulations. We show that multiyear variability in Southern Ocean sea surface temperatures (SSTs) can in turn influence oceanic and atmospheric conditions in the tropics on short (atmospheric) time-scales. We argue that the strength and pattern of SO-tropical teleconnections depends on the intensity of SO deep convection. Periodic convection in the SO is a feature of most CMIP5 models under preindustrial forcing (deLavergne et al., 2014). Models show a wide distribution in the spatial extent, periodicity and intensity of their SO convection, with some models convecting most of the time, and some showing very little convection. In a highly convective coupled model, we find that multidecadal variability in SO and global SSTs, as well as SO heat storage are driven by Weddell Sea convective variability, with convective decades relatively warm due to the heat released from the deep southern ocean and non-convective decades cold due to the subsurface storage of heat. Furthermore, pulses of SO convection drive SST and sea ice variations, influencing absorbed shortwave and emitted longwave radiation, wind, cloud and precipitation patterns, with climatic implications for the low latitudes via fast atmospheric teleconnections. We suggest that these high-low latitude teleconnection mechanisms are relevant for understanding hiatus decades. Additionally, Southern Ocean deep convection varied significantly during past, natural climate changes such as during the last deglaciation. Weddell Sea open convection was recently weakened, likely as a consequence of anthropogenic forcing and the resulting surface freshening. Our study opens up the

This thesis deals with topology optimisation for coupled convection problems. The aim is to extend and apply topology optimisation to steady-state conjugate heat transfer problems, where the heat conduction equation governs the heat transfer in a solid and is coupled to thermal transport...... in a surrounding uid, governed by a convection-diffusion equation, where the convective velocity field is found from solving the isothermal incompressible steady-state Navier-Stokes equations. Topology optimisation is also applied to steady-state natural convection problems. The modelling is done using stabilised...... finite elements, the formulation and implementation of which was done partly during a special course as prepatory work for this thesis. The formulation is extended with a Brinkman friction term in order to facilitate the topology optimisation of fluid flow and convective cooling problems. The derived...

To interpret the high-quality data produced from recent space-missions it is necessary to study convection under realistic stellar conditions. We describe the multi-dimensional, time implicit, fully compressible, hydrodynamic, implicit large eddy simulation code MUSIC. We use MUSIC to study convection during an early stage in the evolution of our sun where the convection zone covers approximately half of the solar radius. This model of the young sun possesses a realistic stratification in density, temperature, and luminosity. We approach convection in a stellar context using extreme value theory and derive a new model for convective penetration, targeted for one-dimensional stellar evolution calculations. This model provides a scenario that can explain the observed lithium abundance in the sun and in solar-like stars at a range of ages.

Magneto-convection and gravity waves are numerically simulated with a nonlinear, three-dimensional, time-dependent model of a stratified, rotating, spherical fluid shell heated from below. A Solar-like reference state is specified while global velocity, magnetic field, and thermodynamic perturbations are computed from the anelastic magnetohydrodynamic equations. Convective overshooting from the upper (superadiabatic) part of the shell excites gravity waves in the lower (subadiabatic) part. Due to differential rotation and Coriolis forces, convective cell patterns propagate eastward with a latitudinally dependent phase velocity. The structure of the excited wave motions in the stable region is more time-dependent than that of the convective motions above. The magnetic field tends to be concentrated over giant-cell downdrafts in the convective zone but is affected very little by the wave motion in the stable region

We study numerically the nonlinear interactions between chemical reaction and convective fingering in a diffusive boundary layer in a porous medium. The reaction enhances stability by consuming a solute that is unstably distributed in a gravitational field. We show that chemical reaction profoundly changes the dynamics of the system, by introducing a steady state, shortening the evolution time, and altering the spatial patterns of velocity and concentration of solute. In the presence of weak reaction, finger growth and merger occur effectively, driving strong convective currents in a thick layer of solute. However, as the reaction becomes stronger, finger growth is inhibited, tip-splitting is enhanced and the layer of solute becomes much thinner. Convection enhances the mass flux of solute consumed by reaction in the boundary layer but has a diminishing effect as reaction strength increases. This nonlinear behavior has striking differences to the density fingering of traveling reaction fronts, for which stronger chemical kinetics result in more effective finger merger owing to an increase in the speed of the front. In a boundary layer, a strong stabilizing effect of reaction can maintain a long-term state of convection in isolated fingers of wavelength comparable to that at onset of instability.

In this paper a parametric study of the fundamental exchange processes for energy, mass and momentum between the liquid and gas phases of multicomponent liquid vaporizing droplets is presented. The model, which examines an isolated, vaporizing, multicomponent droplet in an axisymmetric, convecting environment, considers the different volatilities of the liquid components, the alteration of the liquid-phase properties due to the spatial/temporal variations of the species concentrations and also the effects of multicomponent diffusion. In addition, the model accounts for variable thermophysical properties, surface blowing and droplet surface regression due to vaporization, transient droplet heating with internal liquid circulation, and finally droplet deceleration with respect to the free flow due to drag. The numerical calculation employs finite-difference techniques and an iterative solution procedure that provides time-varying spatially-resolved data for both phases. The effects of initial droplet composition, ambient temperature, initial Reynolds number (based on droplet diameter), and volatility differential between the two liquid components are investigated for a liquid droplet consisting of two components with very different volatilities. It is found that mixtures with higher concentration of the less volatile substance actually vaporize faster on account of intrinsically higher liquid heating rates

Finite amplitude convection with a continuous finite bandwidth of modes in a horizontal mushy layer during the solidification of binary alloys is investigated. We analyze the nonlinear convection for values of the Rayleigh number close to its critical value by using multiple scales and perturbation techniques. Applying a combined temporal and spatial evolution approach, we determine a set of three coupled differential equations for the amplitude functions of the convective modes. A large number of new subcritical or supercritical stable solutions to these equations in the form of steady rolls and hexagons with different horizontal length scales are detected. We find, in particular, that depending on the parameter values and on the magnitude and direction of the wave number vectors for the amplitude functions, hexagons with down-flow or up-flow at the cells’ centers or rolls can be stable. Rolls or hexagons with longer horizontal wave length can be stable at higher amplitudes, and there are cases where hexagons are unstable for any value of the Rayleigh number, while rolls are stable only for the values of the Rayleigh number beyond some value. We also detected new stable and irregular flow patterns with two different horizontal scales in the form of superposition of either two sets of hexagons or two sets of inclined rolls. (paper)

Current generation vector machines are providing for the first time the computing power needed to treat planetary mantle convection in a fully three-dimensional fashion. A numerical technique known as multigrid has been implemented in spherical geometry using a hierarchy of meshes constructed from the regular icosahedron to yield a highly efficient three-dimensional compressible Eulerian finite element hydrodynamics formulation. The paper describes the numerical method and presents convectionsolutions for the mantles of both the earth and the Moon. In the case of the Earth, the convection pattern is characterized by upwelling in narrow circular plumes originating at the core-mantle boundary and by downwelling in sheets or slabs derived from the cold upper boundary layer. The preferred number of plumes appears to be on the order of six or seven. For the Moon, the numerical results indicate that development of a predominately L = 2 pattern in later lunar history is a plausible explanation for the present large second-degree non-hydrostatic component in the lunar figure

A one dimensional model is presented together with experiments, which describe the natural convective flow in closed loops heated at the bottom and cooled in the upper semicircle. Starting from a single loop, mechanical and thermal coupling with a second loop is discussed. The experiments and the theoretical model both concurrently demonstrate that the investigated natural convection is clearly influenced by non-linear effects. Beside the variety of stable steady flows there are extensive subcritical ranges of convective flow. In these parameter ranges subcritical instabilities of the steady state flow could occur in the presence of finite amplitude disturbances. However, the supercritical, global unstable range is characterized by chaotic histories of the variables of state. Non-symmetric heating generates an imperfect bifurcation out of the steady solution with zero velocity in the loop. This effect stabilizes the flow in the preferred direction. The flow in the opposite direction only remains stable in a small isolated interval of the heating parameter. Furthermore the calculations with the model equations demonstrate that a stable periodic behaviour of the flow is possible in a small parameter window. However, it has not been possible to verify this particular effect in the experiments conducted to date. (orig./GL) [de

Full Text Available Recent studies of the dynamic evolution of magnetic flux tubes in the solar convection zone are reviewed with focus on emerging flux tubes responsible for the formation of solar active regions. The current prevailing picture is that active regions on the solar surface originate from strong toroidal magnetic fields generated by the solar dynamo mechanism at the thin tachocline layer at the base of the solar convection zone. Thus the magnetic fields need to traverse the entire convection zone before they reach the photosphere to form the observed solar active regions. This review discusses results with regard to the following major topics: 1. the equilibrium properties of the toroidal magnetic fields stored in the stable overshoot region at the base of the convection zone, 2. the buoyancy instability associated with the toroidal magnetic fields and the formation of buoyant magnetic flux tubes, 3. the rise of emerging flux loops through the solar convective envelope as modeled by the thin flux tube calculations which infer that the field strength of the toroidal magnetic fields at the base of the solar convection zone is significantly higher than the value in equipartition with convection, 4. the minimum twist needed for maintaining cohesion of the rising flux tubes, 5. the rise of highly twisted kink unstable flux tubes as a possible origin of d -sunspots, 6. the evolution of buoyant magnetic flux tubes in 3D stratified convection, 7. turbulent pumping of magnetic flux by penetrative compressible convection, 8. an alternative mechanism for intensifying toroidal magnetic fields to significantly super-equipartition field strengths by conversion of the potential energy associated with the superadiabatic stratification of the solar convection zone, and finally 9. a brief overview of our current understanding of flux emergence at the surface and post-emergence evolution of the subsurface magnetic fields.

This paper studies the heat transfer analysis caused due to free convection in a vertically oscillating cylinder. Exact solutions are determined by applying the Laplace and finite Hankel transforms. Expressions for temperature distribution and velocity field corresponding to cosine and sine oscillations are obtained. The solutions that have been obtained for velocity are presented in the forms of transient and post-transient solutions. Moreover, these solutions satisfy both the governing differential equation and all imposed initial and boundary conditions. Numerical computations and graphical illustrations are used in order to study the effects of Prandtl and Grashof numbers on velocity and temperature for various times. The transient solutions for both cosine and sine oscillations are also computed in tables. It is found that, the transient solutions are of considerable interest up to the times t = 15 for cosine oscillations and t = 1.75 for sine oscillations. After these moments, the transient solutions can be neglected and, the fluid moves according with the post-transient solutions.

Full Text Available The article shows the results of mathematical modeling of convective heat transfer in the low-temperature storage of liquefied natural gas. Regime of natural convection in an enclosure with different intensity of the heat flux at the external borders are investigated. Was examined two-dimensional nonstationary problem within the model of Navier-Stokes in dimensionless variables “vorticity - stream function - temperature”. Distributions of hydrodynamic parameters and temperatures that characterize the basic regularities of the processes are obtained. Circulating flows are determined and carried out the analysis of vortices formation mechanism and the temperature distribution in solution at conditions of natural convection when the Grashof number (Gr = 106. A significant influence of heat transfer rate on solutions boundary on flow structure and temperature field in LNG storage tanks.

In this paper we propose a new acoustic-convective splitting-based numerical scheme for the Kapila five-equation two-phase flow model. The splitting operator decouples the acoustic waves and convective waves. The resulting two submodels are alternately numerically solved to approximate the solution of the entire model. The Lagrangian form of the acoustic submodel is numerically solved using an HLLC-type Riemann solver whereas the convective part is approximated with an upwind scheme. The result is a simple method which allows for a general equation of state. Numerical computations are performed for standard two-phase shock tube problems. A comparison is made with a non-splitting approach. The results are in good agreement with reference results and exact solutions.

The use of actively convected liquid metals with j × B force is proposed to facilitate heat handling by the divertor, a challenging issue associated with magnetic fusion experiments such as ITER. This issue will be aggravated even more for DEMO and power reactors because the divertor heat load will be significantly higher and yet the use of copper would not be allowed as the heat sink material. Instead, reduced activation ferritic/martensitic steel alloys with heat conductivities substantially lower than that of copper, will be used as the structural materials. The present proposal is to fill the lower part of the vacuum vessel with liquid metals with relatively low melting points and low chemical activities including Ga and Sn. The divertor modules, equipped with electrodes and cooling tubes, are immersed in the liquid metal. The electrode, placed in the middle of the liquid metal, can be biased positively or negatively with respect to the module. The j × B force due to the current between the electrode and the module provides a rotating motion for the liquid metal around the electrodes. The rise in liquid temperature at the separatrix hit point can be maintained at acceptable levels from the operation point of view. As the rotation speed increases, the current in the liquid metal is expected to decrease due to the v × B electromotive force. This rotating motion in the poloidal plane will reduce the divertor heat load significantly. Another important benefit of the convected liquid metal divertor is the fast recovery from unmitigated disruptions. Also, the liquid metal divertor concept eliminates the erosion problem. (letter)

We report experimental results on the heat transfer and instability onset of a Rayleigh-Bénard convection cell of aspect ratios 6:3:1 filled with a high Prandtl aqueous solution of glycerol under feedback control. We investigate the transient and stationary response of both local temperature readings and heat transfer fluxes on the Rayleigh Bénard cell in both conductive and convective states when we perform two independent feedback control actions on both hot and cold walls. We evaluate the performance of both controllers to maintain a temperature gradient independently if the system is below or above the convection threshold. As the convection cell can be rotated at 180° about the shorter axis of the cell, it was possible to perform transitions between thermal conduction and convection regimes and vice versa under a constant temperature difference maintained by both independent controllers. The experimental setup provided an accurate measurement of the critical Rayleigh number and the evolution of the Nusselt number as a function of the Rayleigh number in the moderately supercritical regime (R a cellular convection pattern formed by 6 transverse rolls throughout the range of Rayleigh numbers.

This paper is devoted to a numerical investigation of the free convection flow about a horizontal cylinder maintained at 0 °C in a water ambient close to the point of maximum density. Complete numerical solutions covering both the transient as well as steady state have been obtained. Principal results indicate that the proximity of the ambient temperature to the point of maximum density plays an important role in the type of convection pattern that may be obtained. When the ambient temperature is within 4.7 °Csolutions with an initially quasiperiodic behavior which persist for a long time have been observed. Multiple solutions have been observed when the above range of ambient temperature is approached from either side. The results of the computations have been compared with published experimental and numerical data with satisfactory agreement being obtained.

Of obvious importance to the study and engineering of a seabed disposal is the determination of the temperature and fluid flow fields existing in the sediment layer and the perturbation of these fields due to the implantation of localized heat sources. The fluid mechanical and heat transfer process occurring in oceanic sediments may be characterized as free (or natural) convection in a porous material. In the case of an undisturbed sediment layer, the driving force for the natural circulation of pore water comes from the geothermal heat flux. Current theories for heat flow from the sea floor suggest the possibility of large scale hydrothermal circulation in the oceanic crust (see e.g., Ribando, et al. 1976) which is in turn coupled with a convection process in the overlying sediment layer (Anderson 1980, Anderson, et al. 1979). The introduction of a local heat source, such as a waste canister, into a saturated sediment layer would by itself initiate a convection process due to buoyancy forces. Since the mathematical description of natural convection in a porous medium is of sufficient complexity to preclude the use of most analytic methods of analysis, approximate numerical procedures are often employed. In the following sections, a particular type of numerical method is described that has proved useful in the solution of a variety of porous flow problems. However, rather than concentrate on the details of the numerical algorithm the main emphasis of the presentation will be on the types of problems and results that are encountered in the areas of oceanic heat flow and seabed waste disposal

The solution of the optimization problem for longitudinal convective fins of constant thickness, triangular or parabolic profile, and uniform internal heat generation, is presented. The cases considered are those of a given heat generation density, total heat generation and heat generation per unit width of the fin, when either the heat dissipation or the width of the fin is prescribed. The results are set forth in a nondimensional form, which are presented graphically. The effect of the fin's thermal conductivity upon the optimum dimensions is discussed, and limiting values for the heat generation and the heat dissipation, which may be imposed on the fin for a feasible optimization, are also obtained. (Auth.)

The steady laminar natural convection of a fluid having chemical reaction of order n past a semi-infinite vertical plate is considered. The solution of the problem by means of one-parameter group method reduces the number of independent variables by one leading to a system of nonlinear ordinary differential equations. Two different similarity transformations are found. In each case the set of differential equations are solved numerically using Runge-Kutta and the shooting method. For each transformation different Schmidt numbers and chemical reaction orders are tested.

A new, satellite-based methodology is developed to evaluate convective mass flux and large-scale total mass flux. To derive the convective mass flux, candidate profiles of in-cloud vertical velocity are first constructed with a simple plume model under the constraint of ambient sounding and then narrowed down to the solution that matches satellite-derived cloud top buoyancy. Meanwhile, the large-scale total mass flux is provided separately from satellite soundings by a method developed previously. All satellite snapshots are sorted into a composite time series that delineates the evolution of a vigorous and organized convective system. Principal findings are the following. First, convective mass flux is modulated primarily by convective cloud cover, with the intensity of individual convection being less variable over time. Second, convective mass flux dominates the total mass flux only during the early hours of the convective evolution; as convective system matures, a residual mass flux builds up in the mass flux balance that is reminiscent of stratiform dynamics. The method developed in this study is expected to be of unique utility for future observational diagnosis of tropical convective dynamics and for evaluation of global climate model cumulus parameterizations in a global sense.

Convective motions in moist saturated air are accompanied by the release of latent heat of condensation. Taking this effect into account, we consider the problem of convective instability of a moist saturated air layer, generalizing the formulation of the classical Rayleigh problem. An analytic solution demonstrating the fundamental difference between moist convection and Rayleigh convection is obtained. Upon losing stability in the two-dimensional case, localized convective rolls or spatially periodic chains of rollers with localized areas of upward motion evolve. In the case of axial symmetry, the growth of localized convective vortices with circulation characteristic of tropical cyclones (hurricanes) is possible at the early stages of development and on the scale of tornados to tropical cyclones. (methodological notes)

Convective vortices are common features of atmospheres that absorb lower-entropy-energy at higher temperatures than they reject higher-entropy-energy to space. These vortices range from small to large-scale and play an important role in the vertical transport of heat, momentum, and tracer species. Thus, the development of theoretical models for convective vortices is important to our understanding of some of the basic features of planetary atmospheres. The heat engine framework is a useful tool for studying convective vortices. However, current theories assume that convective vortices are reversible heat engines. Since there are questions about how reversible real atmospheric heat engines are, their usefulness for studying real atmospheric vortices is somewhat controversial. In order to reduce this problem, a theory for convective vortices that includes irreversible processes is proposed. The paper's main result is that the proposed theory provides an expression for the pressure drop along streamlines that includes the effects of irreversible processes. It is shown that a simplified version of this expression is a generalization of Bernoulli's equation to convective circulations. It is speculated that the proposed theory not only explains the intensity, but also sheds light on other basic features of convective vortices such as their physical appearance.

The dynamo equation which represents the longitudinally averaged magnetohydrodynamical action of the global convection influenced by the rotation in the solar convection zone is solved numerically to simulate the solar cycle as an initial boundary-value problem. The radial and latitudinal structure of the dynamo action is parametrized in accordance with the structure of the rotation, and of the global convection especially in such a way as to represent the presence of the two cells of the regeneration action in the radial direction in which the action has opposite signs, which is typical of the regeneration action of the global convection. A nonlinear process is included by assuming that part of the magnetic field energy is dissipated when the magnetic field strength exceeds some critical value; the formation of active regions and subsequent dissipations are thus simulated. By adjusting the parameters within a reasonable range, oscillatory solutions are obtained to simulate the solar cycle with the period of the right order of magnitude and with the patterns of evolution of the latitudinal distribution of the toroidal component of the magnetic field similar to the observed Butterfly Diagram of sunspots. The evolution of the latitudinal distribution of the radial component of the magnetic field shows patterns similar to the Butterfly Diagram, but having two branches of different polarity in each hemisphere. The development of the radial structure of the magnetic field associated with the solar cycle is presented. The importance of the poleward migrating branch of the Butterfly Diagram is emphasized in relation to the relative importance of the role of the latitudinal and radial shears of the differential rotation

Rotating convection is ubiquitous in the natural universe, and is likely responsible for planetary processes such magnetic field generation. Rapidly rotating convection is typically organized by the Coriolis force into tall, thin, coherent convection columns which are aligned with the axis of rotation. This organizational effect of rotation is thought to be responsible for the strength and structure of magnetic fields generated by convecting planetary interiors. As thermal forcing is increased, the relative influence of rotation weakens, and fully three-dimensional convection can exist. It has long been assumed that rotational effects will dominate convection dynamics when the ratio of buoyancy to the Coriolis force, the convective Rossby number, Roc, is less than unity. We investigate the influence of rotation on turbulent Rayleigh-Benard convection via a suite of coupled laboratory and numerical experiments over a broad parameter range: Rayleigh number, 10310; Ekman number, 10-6≤ E ≤ ∞; and Prandtl number, 1≤ Pr ≤ 100. In particular, we measure heat transfer (as characterized by the Nusselt number, Nu) as a function of the Rayleigh number for several different Ekman and Prandtl numbers. Two distinct heat transfer scaling regimes are identified: non-rotating style heat transfer, Nu ~ Ra2/7, and quasigeostrophic style heat transfer, Nu~ Ra6/5. The transition between the non-rotating regime and the rotationally dominant regime is described as a function of the Ekman number, E. We show that the regime transition depends not on the global force balance Roc, but on the relative thicknesses of the thermal and Ekman boundary layers. The transition scaling provides a predictive criterion for the applicability of convection models to natural systems such as Earth's core.

The problem of free convection in a thin porous contour, placed in uniform impermeable massif is considered. The approximate analitical solution of conjugate problem is obtained. The critical Rayleigh number is determined, by exceeding of which the steady fluid circulation in an annulus is established. The computations of abnormal heat flow near surface are carried out, stipulated by thermoconvection in a contour.

In this paper, A asymptotic numerical method for the steady-state Convection diffusion equation is proposed, which need not take very fine mesh size in the neighbourhood of the boundary layer. Numerical computation for model problem show that we can obtain the numerical solution in the boundary layer with moderate step size

The present study is directed at developing a finite element computer program for solution of decoupled convective/conductive heat transfer problems. Penalty function formulation has been used to solve momentum equations and subsequently transient energy equation is solved using modified Crank-Nicolson method. The optimal upwinding scheme has been employed in energy equation to remove oscillations at high Peclet number. (author)

Unsteady free convection flow of a viscous incompressible electrically conducting fluid between two heated conducting vertical parallel plates subjected to a uniform transverse magnetic field is considered. The approximate analytical solutions for velocity, induced field and temperature distribution are obtained for small and large values of magnetic Reynolds number. The problem is also extended to thermometric case. (author)

In this paper we study the instability of the traveling waves of the convective-diffusive Cahn-Hilliard equation. We prove that it is nonlinearly unstable under H 2 perturbations, for some traveling wave solution that is asymptotic to a constant as x→∞

Deep convection forms the upward branches of all large-scale circulations in the tropics. Understanding what controls the form and intensity of vertical convective mass fluxes is thus key to understanding tropical weather and climate. These mass fluxes and the corresponding conditions supporting them have been measured by recent field programs (TPARC/TCS08, PREDICT, HS3) in tropical disturbances considered to be possible tropical storm precursors. In reality, this encompasses most strong convection in the tropics. The measurements were made with arrays of dropsondes deployed from high altitude. In some cases Doppler radar provided additional measurements. The results are in some ways surprising. Three factors were found to control the mass flux profiles, the strength of total surface heat fluxes, the column-integrated relative humidity, and the low to mid-tropospheric moist convective instability. The first two act as expected, with larger heat fluxes and higher humidity producing more precipitation and stronger lower tropospheric mass fluxes. However, unexpectedly, smaller (but still positive) convective instability produces more precipitation as well as more bottom-heavy convective mass flux profiles. Furthermore, the column humidity and the convective instability are anti-correlated, at least in the presence of strong convection. On spatial scales of a few hundred kilometers, the virtual temperature structure appears to be in dynamic balance with the pattern of potential vorticity. Since potential vorticity typically evolves on longer time scales than convection, the potential vorticity pattern plus the surface heat fluxes then become the immediate controlling factors for average convective properties. All measurements so far have taken place in regions with relatively flat sea surface temperature (SST) distributions. We are currently seeking funding for a measurement program in the tropical east Pacific, a region that exhibits strong SST gradients and

The results of this project are best described by the papers and dissertations that resulted from the work. They are included in their entirety in this document. They are: (1) Jeff Harris PhD dissertation (focused mainly on forced convection); (2) Blake Lance PhD dissertation (focused mainly on mixed and transient convection). This dissertation is in multi-paper format and includes the article currently submitted and one to be submitted shortly; and, (3) JFE paper on CFD Validation Benchmark for Forced Convection.

The properties of convective cells and the diffusion resulting from such cells are significantly influenced by an inhomogeneity in the extermal confining magnetic field, such as that in toroidal plasmas. The convective diffusion in the presence of a field inhomogeneity is estimated. For a thermal background, this diffusion is shown to be substantially smaller than classical collisional diffusion. For a model nonthermal background, the diffusion is estimated, for typical parameters, to be at most of the order of collisional diffusion. The model background employed is based on spectra observed in numerical simulations of drift-wave-driven convective cells

The results of this project are best described by the papers and dissertations that resulted from the work. They are included in their entirety in this document. They are: (1) Jeff Harris PhD dissertation (focused mainly on forced convection); (2) Blake Lance PhD dissertation (focused mainly on mixed and transient convection). This dissertation is in multi-paper format and includes the article currently submitted and one to be submitted shortly; and, (3) JFE paper on CFD Validation Benchmark for Forced Convection.

This paper describes research done to apply the Fractional Step Method to finite-element simulations of natural convective flows in pure liquids, permeable media, and in a directionally solidified metal alloy casting. The Fractional Step Method has been applied commonly to high Reynold's number flow simulations, but is less common for low Reynold's number flows, such as natural convection in liquids and in permeable media. The Fractional Step Method offers increased speed and reduced memory requirements by allowing non-coupled solution of the pressure and the velocity components. The Fractional Step Method has particular benefits for predicting flows in a directionally solidified alloy, since other methods presently employed are not very efficient. Previously, the most suitable method for predicting flows in a directionally solidified binary alloy was the penalty method. The penalty method requires direct matrix solvers, due to the penalty term. The Fractional Step Method allows iterative solution of the finite element stiffness matrices, thereby allowing more efficient solution of the matrices. The Fractional Step Method also lends itself to parallel processing, since the velocity component stiffness matrices can be built and solved independently of each other. The finite-element simulations of a directionally solidified casting are used to predict macrosegregation in directionally solidified castings. In particular, the finite-element simulations predict the existence of 'channels' within the processing mushy zone and subsequently 'freckles' within the fully processed solid, which are known to result from macrosegregation, or what is often referred to as thermo-solutalconvection. These freckles cause material property non-uniformities in directionally solidified castings; therefore many of these castings are scrapped. The phenomenon of natural convection in an alloy under-going directional solidification, or thermo-solutalconvection, will be explained. The

This paper presents a study of the Dual Reciprocity Boundary Element Method (DRBEM) for the laminar heat convection problem in a concentric annulus with constant heat flux boundary condition. DRBEM is one of the most successful technique used to transform the domain integrals arising from the nonhomogeneous term of the poisson equation into equivalent boundary only integrals. This recently developed and highly efficient numerical method is tested for the solution accuracy of the fluid flow and heat transfer study in a concentric annulus. Since their exact solutions are available, DRBEM solutions are verified with different number of boundary element discretization and internal points. The results obtained in this study are discussed with the relative error percentage of velocity and temperature solutions, and potential applicability of the method for the more complicated heat convection problems with arbitrary duct geometries

The 8 november 2000, the SFT (Societe Francaise de Thermique) organized a technical day on the convection in complex shaped vessels. Nine papers have been presented in the domains of the heat transfers, the natural convection, the fluid distribution, the thermosyphon effect, the steam flow in a sterilization cycle and the transformers cooling. Eight papers are analyzed in ETDE and one paper dealing with the natural convection in spent fuels depository is analyzed in INIS. (A.L.B.)

Numerical calculations have been carried out of steady, symmetric, three-dimensional modes of convection in internally heated, infinite Prandtl number, Boussinesq fluids at a Rayleigh number of 1.4x10 4 in a spherical shell with inner/outer radius of 0.55 and in a 3x3x1 rectangular box. Multiple patterns of convection occur in both geometries. In the Cartesian geometry the patterns are dominated by cylindrical cold downflows and a broad hot upwelling. In the spherical geometry the patterns consist of cylindrical cold downwellings centered either at the vertices of a tetrahedron or the centers of the faces of a cube. The cold downflow cylinders are immersed in a background of upwelling within which there are cylindrical hot concentrations (plumes) and hot halos around the downflows. The forced hot upflow return plumes of internally heated spherical convection are fundamentally different from the buoyancy-driven plumes of heated from below convection

Deep convective systems are destructive weather phenomena that annually cause many deaths and injuries as well as much damage, thereby accounting for major economic losses in several countries. The number and intensity of such phenomena have increased over the last decades in some areas of the globe. Damage is mostly caused by strong winds and heavy rain parameters that are strongly connected to the structure of the particular storm. Convection over land is usually stronger and deeper than over the ocean and some convective systems, known as supercells, also develop tornadoes through processes that remain mostly unclear. The intensity forecast and monitoring of convective systems is one of the major challenges for meteorology because in situ measurements during extreme events are too sparse or unreliable and most ongoing satellite missions do not provide suitable time/space coverage.

... efficiency as well as the knock and emission characteristics. The ignition event is clearly controlled by the chemical reactions of fuel oxidation and the fluid mechanics of convective and diffusive transport...

The heat generation and fluid convection induced by plasmonic nanostructures is attractive for optofluidic applications. However, previously published theoretical studies predict only nanometre per second fluid velocities that are inadequate for microscale mass transport. Here we show both theoretically and experimentally that an array of plasmonic nanoantennas coupled to an optically absorptive indium-tin-oxide (ITO) substrate can generate >micrometre per second fluid convection. Crucially, the ITO distributes thermal energy created by the nanoantennas generating an order of magnitude increase in convection velocities compared with nanoantennas on a SiO2 base layer. In addition, the plasmonic array alters absorption in the ITO, causing a deviation from Beer-Lambert absorption that results in an optimum ITO thickness for a given system. This work elucidates the role of convection in plasmonic optical trapping and particle assembly, and opens up new avenues for controlling fluid and mass transport on the micro- and nanoscale.

The organization of convection is ubiquitous, but its physical understanding remains limited. One particular type of organization is the spatial self-aggregation of convection, taking the form of cloud clusters, or tropical cyclones in the presence of rotation. We show that several physical processes can give rise to self-aggregation and highlight the key features responsible for it, using idealized simulations. Longwave radiative feedbacks yield a "radiative aggregation." In that case, sufficient spatial variability of radiative cooling rates yields a low-level circulation, which induces the upgradient energy transport and radiative-convective instability. Not only do vertically integrated radiative budgets matter but the vertical profile of cooling is also crucial. Convective aggregation is facilitated when downdrafts below clouds are weak ("moisture-memory aggregation"), and this is sufficient to trigger aggregation in the absence of longwave radiative feedbacks. These results shed some light on the sensitivity of self-aggregation to various parameters, including resolution or domain size.

This thesis is concerned with the use of whistler duct tracking as a diagnostic for the behaviour of plasma in the plasmasphere. As a setting for the results given in the thesis, a broad review is presented which embraces pertinent aspects of previous experimental and theoretical studies of the plasmasphere. From a study of 24 hours of continuous whistler data recorded at Sanae, (L = 3,98), it is shown that associated with quiet magnetic conditions (Av Ksub(p)=1), there exists two plasmasphere bulges centred on about 1700 and 0100 UT. There is evidence that these plasmasphere bulge structures are part of a ground-state or reference base drift pattern. Electric field measurements provide some evidence that quiet time plasmasphere drift behaviour is controlled by the internal ionospheric current systems of dynamo origin, rather than being controlled by magnetospheric convection. Finally, this thesis describes an application of the whistler duct tracking technique to whistler data recorded simultaneously at two ground-based stations (Sanae (L = 3,98) and Halley (L = 4,23)). The identification of common whistler components on each station's data set provides a means of estimating the lifetimes of the associated whistler ducts. Duct lifetimes of as little as 30 minutes are found. Such short lived ducts have important implications for current theories of duct formation

Hence, most of the real nonlinear physical equations possess variable ... evolution of the system with time and second term represents the convective flux term. The ... Travelling wave solutions of nonlinear reaction-diffusion equations are.

The dynamics of drying sunflower cake by a new acoustic-convective method has been studied. Unlike the conventional (thermal-convective) method, the proposed method allows moisture to be extracted from porous materials without applying heat to the sample to be dried. Kinetic curves of drying by the thermal-convective and acoustic-convective methods were obtained and analyzed. The advantages of the acoustic-convective extraction of moisture over the thermal-convective method are discussed. The relaxation times of drying were determined for both drying methods. An intermittent drying mode which improves the efficiency of acoustic-convective extraction of moisture is considered.

Condensible substances are nearly ubiquitous in planetary atmospheres. For the most familiar case—water vapor in Earth’s present climate—the condensible gas is dilute, in the sense that its concentration is everywhere small relative to the noncondensible background gases. A wide variety of important planetary climate problems involve nondilute condensible substances. These include planets near or undergoing a water vapor runaway and planets near the outer edge of the conventional habitable zone, for which CO{sub 2} is the condensible. Standard representations of convection in climate models rely on several approximations appropriate only to the dilute limit, while nondilute convection differs in fundamental ways from dilute convection. In this paper, a simple parameterization of convection valid in the nondilute as well as dilute limits is derived and used to discuss the basic character of nondilute convection. The energy conservation properties of the scheme are discussed in detail and are verified in radiative-convective simulations. As a further illustration of the behavior of the scheme, results for a runaway greenhouse atmosphere for both steady instellation and seasonally varying instellation corresponding to a highly eccentric orbit are presented. The latter case illustrates that the high thermal inertia associated with latent heat in nondilute atmospheres can damp out the effects of even extreme seasonal forcing.

Recently, the research on free convection in vertical ducts has become active again concerning the problem of cooling in nuclear reactor accidents and the cooling of electronic equipment. Generally, in the convection heat transfer in ducts, when the wall temperature is high, the fluid temperature in the ducts conspicuously changes, accordingly, the temperature dependence of the properties cannot be neglected. In this study, about the laminar free convection in parallel plates and a circular pipe having uniform wall temperature, the numerical analysis taking the temperature dependence of all properties into account was carried out, thus the effect of the temperature dependence of properties exerted on free convection heat transfer was clarified, and the relation to the solution in constant properties was examined. Moreover, by introducing a new representative dimension, it was attempted to express mean heat transfer coefficient which is independent of the form of ducts in unified way. The mean Nusselt number of the constant property solution using entrance pressure condition agreed very well with the exact numerical solution. (Kako, I.)

A thermal lattice BGK model with doubled populations is proposed to simulate the two-dimensional natural convection flow in porous media (porous metals). The accuracy of this method is validated by the benchmark solutions. The detailed flow and heat transfer at the pore level are revealed. The effects of pore density (cell size) and porosity on the natural convection are examined. Also the effect of porous media configuration (shape) on natural convection is investigated. The results showed that the overall heat transfer will be enhanced by lowering the porosity and cell size. The square porous medium can have a higher heat transfer performance than spheres due to the strong flow mixing and more surface area.

Results from direct numerical simulations of vertical natural convection at Rayleigh numbers 1.0×10 5 –1.0×10 9 and Prandtl number 0.709 support a generalised applicability of the Grossmann–Lohse (GL) theory, which was originally developed for horizontal natural (Rayleigh–Bénard) convection. In

Paper presents detailed study of spurious steady-state numerical solutions of differential equations that contain nonlinear source terms. Main objectives of this study are (1) to investigate how well numerical steady-state solutions of model nonlinear reaction/convection boundary-value problem mimic true steady-state solutions and (2) to relate findings of this investigation to implications for interpretation of numerical results from computational-fluid-dynamics algorithms and computer codes used to simulate reacting flows.

In the present work, the effects of some parametric values on convective heat transfer coefficients and the thin layer drying process of ginger slices were investigated. Drying was done in the laboratory by using cyclone type convective dryer. The drying air temperature was varied as 40, 50, 60 and 70 °C and the air velocity is 0.8, 1.5 and 3 m/s. All drying experiments had only falling rate period. The drying data were fitted to the twelve mathematical models and performance of these models was investigated by comparing the determination of coefficient ( R 2), reduced Chi-square ( χ 2) and root mean square error between the observed and predicted moisture ratios. The effective moisture diffusivity and activation energy were calculated using an infinite series solution of Fick's diffusion equation. The average effective moisture diffusivity values and activation energy values varied from 2.807 × 10-10 to 6.977 × 10-10 m2/s and 19.313-22.722 kJ/mol over the drying air temperature and velocity range, respectively. Experimental data was used to evaluate the values of constants in Nusselt number expression by using linear regression analysis and consequently, convective heat transfer coefficients were determined in forced convection mode. Convective heat transfer coefficient of ginger slices showed changes in ranges 0.33-2.11 W/m2 °C.

Full Text Available We showed that solutions by the Haar wavelet-quasilinearization technique for the two problems, namely, (i temperature distribution equation in lumped system of combined convection-radiation in a slab made of materials with variable thermal conductivity and (ii cooling of a lumped system by combined convection and radiation are strongly reliable and also more accurate than the other numerical methods and are in good agreement with exact solution. According to the Haar wavelet-quasilinearization technique, we convert the nonlinear heat transfer equation to linear discretized equation with the help of quasilinearization technique and apply the Haar wavelet method at each iteration of quasilinearization technique to get the solution. The main aim of present work is to show the reliability of the Haar wavelet-quasilinearization technique for heat transfer equations.

A solution of the convection-dispersion equation is used to describe the solute breakthrough curves generated in the demonstrations in the companion paper. Estimation of the best fit model parameters (solute velocity, dispersion, and retardation) is illustrated using the method of moments for an example data set. (Author/MDH)

Full Text Available A linear stability analysis is used to investigate the influence of mechanical vibration on the onset of thermosolutal convection in a horizontal porous layer heated and salted from above. Vibrations are considered with arbitrary amplitude and frequency. The Brinkman extended Darcy model is used to describe the flow and the Oberbeck-Boussinesq approximation is employed. Continued fraction method and Floquet theory are used to determine the convective instability threshold. It is found that the solutal Rayleigh number has the stabilizing effect. The existence of a closed disconnected loop of synchronous mode is predicted in the marginal curve for moderate values of solutal Rayleigh number and vibration amplitude.

Linear and nonlinear properties of coupled Shukla-Varma (SV) and convective cell modes in the presence of electron thermal effects are studied in a nonuniform magnetoplasma composed of electrons, ions, and extremely massive and negatively charged immobile dust grains. In the linear case, the modified dispersion relation is given and, in the nonlinear case, stationary solutions of the nonlinear equations that govern the dynamics of coupled SV and convective cell modes are obtained. It is found that electrostatic dipolar and vortex street type solutions can appear in such a plasma. The relevance of the present investigation with regard to the Earth's mesosphere as well as in ionospheric plasmas is also pointed out.

Linear and nonlinear properties of coupled Shukla-Varma (SV) and convective cell modes in the presence of electron thermal effects are studied in a nonuniform magnetoplasma composed of electrons, ions, and extremely massive and negatively charged immobile dust grains. In the linear case, the modified dispersion relation is given and, in the nonlinear case, stationary solutions of the nonlinear equations that govern the dynamics of coupled SV and convective cell modes are obtained. It is found that electrostatic dipolar and vortex street type solutions can appear in such a plasma. The relevance of the present investigation with regard to the Earth's mesosphere as well as in ionospheric plasmas is also pointed out.

Full Text Available The current paper presents a theoretical analysis of the transport of solutes through a fixed-film membrane bioreactor (MBR, immobilised with an active biocatalyst. The dimensionless convection-diffusion equation with variable coefficients was solved analytically and numerically for concentration profiles of the solutes through the MBR. The analytical solution makes use of regular perturbation and accounts for radial convective flow as well as axial diffusion of the substrate species. The Michaelis-Menten (or Monod rate equation was assumed for the sink term, and the perturbation was extended up to second-order. In the analytical solution only the first-order limit of the Michaelis-Menten equation was considered; hence the linearized equation was solved. In the numerical solution, however, this restriction was lifted. The solution of the nonlinear, elliptic, partial differential equation was based on an implicit finite-difference method (FDM. An upwind scheme was employed for numerical stability. The resulting algebraic equations were solved simultaneously using the multivariate Newton-Raphson iteration method. The solution allows for the evaluation of the effect on the concentration profiles of (i the radial and axial convective velocity, (ii the convective mass transfer rates, (iii the reaction rates, (iv the fraction retentate, and (v the aspect ratio.

The conditions under which convective mixing episodes take place between the helium envelopes and the underlying carbon layers in helium-rich white dwarfs are investigated. It is found that, for essentially any value of the initial helium content less than the maximum mass a helium convection zone can have, mixing does occur, and leads, in the vast majority of cases, to an almost pure carbon superficial composition. Mixing products that show only traces of carbon while retaining helium-dominated envelopes are possible only if the initial helium content is quite close to the maximum possible mass of the helium convection zone. In the presence of turbulence, this restriction could be relaxed, however, and the helium-rich lambda4670 stars may possibly be explained in this fashion

Experiments indicate that turbulent free convection over a horizontal surface (e.g. Rayleigh Bénard convection) consists of essentially line plumes near the walls, at least for moderately high Rayleigh numbers. Based on this evidence, we propose here a two-dimensional model for near-wall dynamics in Rayleigh Bénard convection and in general for convection over heated horizontal surfaces. The model proposes a periodic array of steady laminar two-dimensional plumes. A plume is fed on either side by boundary layers on the wall. The results from the model are obtained in two ways. One of the methods uses the similarity solution of Rotem & Classen (1969) for the boundary layer and the similarity solution of Fuji (1963) for the plume. We have derived expressions for mean temperature and temperature and velocity fluctuations near the wall. In the second approach, we compute the two-dimensional flow field in a two-dimensional rectangular open cavity. The number of plumes in the cavity depends on the length of the cavity. The plume spacing is determined from the critical length at which the number of plumes increases by one. The results for average plume spacing and the distribution of r.m.s. temperature and velocity fluctuations are shown to be in acceptable agreement with experimental results.

The existence of outflow and magnetic fields in the inner region of hot accretion flows has been confirmed by observations and numerical magnetohydrodynamic (MHD) simulations. We present self-similar solutions for radiatively inefficient accretion flows (RIAFs) around black holes in the presence of outflow and a global magnetic field. The influence of outflow is taken into account by adopting a radius that depends on mass accretion rate M-dot = M-dot 0 (r/r 0 ) s with s > 0. We also consider convection through a mixing length formula to calculate convection parameter α con . Moreover we consider the additional magnetic field parameters β r,φ,z [ = c 2 r,φ,z /(2c 2 s )], where c 2 r,φ,z are the Alfvén sound speeds in three directions of cylindrical coordinates. Our numerical results show that by increasing all components of the magnetic field, the surface density and rotational velocity increase, but the sound speed and radial infall velocity of the disk decrease. We have also found that the existence of wind will lead to reduction of surface density as well as rotational velocity. Moreover, the radial velocity, sound speed, advection parameter and the vertical thickness of the disk will increase when outflow becomes important in the RIAF. (research papers)

Full Text Available A computer modeling process of three-dimensional forced convection proceeding from computation of thermodynamic parameters of pneumo basic buildings (pneumo supported structures is presented. The mathematical model of numerical computation method of temperature and velocity fields, pressure profile in the object is developed using the package Solid works and is provided by grid methods on specified software. Special Navier–Stokes, Clapeyron–Mendeleev, continuity and thermal-conductivity equations are used to calculate parameters in the building with four supply and exhaust channels. Differential equations are presented by algebraic equation systems, initial-boundary conditions are changed by differential conditions for mesh functions and their solutions are performed by algebraic operations. In this article the following is demonstrated: in pneumo basic buildings convective and heat flows are identical structures near the surfaces in unlimited space, but in single-multiply shells (envelopescirculation lines take place, geometrical sizes of which depend on thermal-physical characteristics of gas(airin envelopes, radiation reaction with heated surfaces of envelopes with sphere, earth surface, neighboring buildings. Natural surveys of pneumo-basic buildings of different purposes were carried out in Minsk, in different cities of Belarus and Russia, including temperature fields of external and internal surfaces of air envelopes, relative humidity, thermal (heatflows, radiation characteristics and others.The results of research work are illustrated with diagrams of temperature, velocity, density and pressure dependent on coordinates and time.

The solution for the natural convection in internally finned horizontal annuli is obtained by using a numerical simulation of time-dependent and two-dimensional governing equations. The fins existing in annuli influence the flow pattern, temperature distribution and heat transfer rate. The variations of the fin configuration suppress or accelerate the free convective effects compared to those of the smooth tubes. The effects of fin configuration, number of fins and ratio of annulus gap width to the inner cylinder radius on the fluid flow and heat transfer in annuli are demonstrated by the distribution of the velocity vector, isotherms and streamlines. The governing equations are solved efficiently by using a parallel implementation. The technique is adopted for reduction of the computation cost. The parallelization is performed with the domain decomposition technique and message passing between sub-domains on the basis of the MPI library. The results from parallel computation reveal in consistency with those of the sequential program. Moreover, the speed-up ratio shows linearity with the number of processor

Natural Convective Heat Transfer from Narrow Plates deals with a heat transfer situation that is of significant practical importance but which is not adequately dealt with in any existing textbooks or in any widely available review papers. The aim of the book is to introduce the reader to recent studies of natural convection from narrow plates including the effects of plate edge conditions, plate inclination, thermal conditions at the plate surface and interaction of the flows over adjacent plates. Both numerical and experimental studies are discussed and correlation equations based on the results of these studies are reviewed.

We describe experiments on Benard-Marangoni convection which permit a useful understanding of the main concepts involved in this phenomenon such as, for example, Benard cells, aspect ratio, Rayleigh and Marangoni numbers, Crispation number and critical conditions. In spite of the complexity of convection theory, we carry out a simple and introductory analysis which has the additional advantage of providing very suggestive experiments. As a consequence, we recommend our device for use as a laboratory experiment for undergraduate students of the thermodynamics of nonlinear and fluid physics

Partial convection of light by moving media was predicted by Fresnel and verified by Fizeau, Zeeman and others. It is accepted as an important argument in favour of the Special Theory of Relativity. The suggestion is made here that the convection is partial only when the propagating medium is moved with respect to its electrically earthed surroundings and that it would be total if an earthed shield was co-moving with the medium. This is based on a reinterpretation of Maxwell's equations wherein they are seen as macroscopic relationships that are in each case valid only in respect of a particular inertial frame of reference, the local electrical earth frame. (Auth.)

We describe experiments on Benard-Marangoni convection which permit a useful understanding of the main concepts involved in this phenomenon such as, for example, Benard cells, aspect ratio, Rayleigh and Marangoni numbers, Crispation number and critical conditions. In spite of the complexity of convection theory, we carry out a simple and introductory analysis which has the additional advantage of providing very suggestive experiments. As a consequence, we recommend our device for use as a laboratory experiment for undergraduate students of the thermodynamics of nonlinear and fluid physics.

stabilised finite elements implemented in a parallel multiphysics analysis and optimisation framework DFEM [1], developed and maintained in house. Focus is put on control of the temperature field within the solid structure and the problems can therefore be seen as conjugate heat transfer problems, where heat...... conduction governs in the solid parts of the design domain and couples to convection-dominated heat transfer to a surrounding fluid. Both loosely coupled and tightly coupled problems are considered. The loosely coupled problems are convection-diffusion problems, based on an advective velocity field from...

Recently a new thermal lattice Bhatnagar-Gross-Krook fluid model was suggested by the authors. In this study, this new model was applied into the numerical simulation of natural convection, namely the Rayleigh Benard flow. The critical number for the onset of convective phenomenon was numerically measured and compared with that of theoretical prediction. A gravity dependent deviation was found in the numerical simulation, which is explained as an unavoidable consequence of the incorporation of gravity force in the lattice BGK system. (author)

The convective transport of heat and moisture plays a key role in the climate system, but the transport is typically parameterized in models. Here, we aim at the simplest possible physical representation and treat convective heat fluxes as the result of a heat engine. We combine the well-known Carnot limit of this heat engine with the energy balances of the surface-atmosphere system that describe how the temperature difference is affected by convective heat transport, yielding a maximum power limit of convection. This results in a simple analytic expression for convective strength that depends primarily on surface solar absorption. We compare this expression with an idealized grey atmosphere radiative-convective (RC) model as well as Global Circulation Model (GCM) simulations at the grid scale. We find that our simple expression as well as the RC model can explain much of the geographic variation of the GCM output, resulting in strong linear correlations among the three approaches. The RC model, however, shows a lower bias than our simple expression. We identify the use of the prescribed convective adjustment in RC-like models as the reason for the lower bias. The strength of our model lies in its ability to capture the geographic variation of convective strength with a parameter-free expression. On the other hand, the comparison with the RC model indicates a method for improving the formulation of radiative transfer in our simple approach. We also find that the latent heat fluxes compare very well among the approaches, as well as their sensitivity to surface warming. What our comparison suggests is that the strength of convection and their sensitivity in the climatic mean can be estimated relatively robustly by rather simple approaches.

For pt.I see ibid., vol.193, p.105-18, 1999. Rigorous numerical solution of natural convection heat transfer, from a horizontal cylinder with uniform surface heat flux or with uniform surface temperature, to liquid sodium was derived by solving the fundamental equations for laminar natural convection heat transfer without the boundary layer approximation. It was made clear that the local and average Nusselt numbers experimentally obtained and reported in part 1 of this paper were described well by the numerical solutions for uniform surface heat fluxes, but that those for uniform surface temperatures could not describe the angular distribution of the local Nusselt numbers and about 10% underpredicted the average Nusselt numbers. Generalized correlation for natural convection heat transfer from a horizontal cylinder with a uniform surface heat flux in liquid metals was presented based on the rigorous theoretical values for a wide range of Rayleigh numbers. It was confirmed that the correlation can describe the authors' and other workers' experimental data on horizontal cylinders in various kinds of liquid metals for a wide range of Rayleigh numbers. Another correlation for a horizontal cylinder with a uniform surface temperature in liquid metals, which may be applicable for special cases such as natural convection heat transfer in a sodium-to-sodium heat exchanger etc. was also presented based on the rigorous theoretical values for a wide range of Rayleigh numbers. These correlations can also describe the rigorous numerical solutions for non-metallic liquids and gases for the Prandtl numbers up to 10. (orig.)

Steady and transient analytical investigation with the Galerkin method has been performed on natural convection in a horizontal porous annulus heated from the inner surface. Three families of convergent solutions, appearing one after another with increasing RaDa numbers, were obtained corresponding to different initial conditions. Despite the fact that the flow structures of two branching solutions are quite different, there exists a critical RaDa number at which their overall heat transfer rates have the same value. The bifurcation point was determined numerically, which coincided very well with that from experimental observation. The solutions in which higher wavenumber modes are dominant agree better with experimental data of overall heat transfer

In this article, the mixed convective heat transfer to Sisko fluid over a radially stretching surface in the presence of convective boundary conditions is investigated. The viscous dissipation and thermal radiation effects are also taken into account. The suitable transformations are applied to convert the governing partial differential equations into a set of nonlinear coupled ordinary differential equations. The analytical solution of the governing problem is obtained by using the homotopy analysis method (HAM). Additionally, these analytical results are compared with the numerical results obtained by the shooting technique. The obtained results for the velocity and temperature are analyzed graphically for several physical parameters for the assisting and opposing flows. It is found that the effect of buoyancy parameter is more prominent in case of the assisting flow as compared to the opposing flow. Further, in tabular form the numerical values are given for the local skin friction coefficient and local Nusselt number. A remarkable agreement is noticed by comparing the present results with the results reported in the literature as a special case.

In this article, the mixed convective heat transfer to Sisko fluid over a radially stretching surface in the presence of convective boundary conditions is investigated. The viscous dissipation and thermal radiation effects are also taken into account. The suitable transformations are applied to convert the governing partial differential equations into a set of nonlinear coupled ordinary differential equations. The analytical solution of the governing problem is obtained by using the homotopy analysis method (HAM). Additionally, these analytical results are compared with the numerical results obtained by the shooting technique. The obtained results for the velocity and temperature are analyzed graphically for several physical parameters for the assisting and opposing flows. It is found that the effect of buoyancy parameter is more prominent in case of the assisting flow as compared to the opposing flow. Further, in tabular form the numerical values are given for the local skin friction coefficient and local Nusselt number. A remarkable agreement is noticed by comparing the present results with the results reported in the literature as a special case

An infinite-dimensional model is derived from the equations of free convection in the Boussinesq-Oberbeck approximation. The velocity field is approximated by a single mode, while the heat-conduction equation is conserved fully. It is shown that, for all supercritical Rayleigh numbers, there exist exactly two secondary convective regimes. The case of ideal convection with zero viscosity and thermal conductivity is examined. The averaging method is used to study convection regimes at high Reynolds numbers. 10 refs.

Instability modes in the form of axially uniform vertical jets, also called “elevator modes,” are known to be the solutions of thermal convection problems for vertically unbounded systems. Typically, their relevance to the actual flow state is limited by three-dimensional breakdown caused by rapid growth of secondary instabilities. We consider a flow of a liquid metal in a vertical duct with a heated wall and strong transverse magnetic field and find elevator modes that are stable and, thus, not just relevant, but a dominant feature of the flow. We then explore the hypothesis suggested by recent experimental data that an analogous instability to modes of slow axial variation develops in finite-length ducts, where it causes large-amplitude fluctuations of temperature. The implications for liquid metal blankets for tokamak fusion reactors that potentially invalidate some of the currently pursued design concepts are discussed.

Full Text Available This study aims to develop a model that accurately represents the convective drying process of textile materials. The mathematical modeling was developed from energy and mass balances and, for the solution of the mathematical model, the technique of finite differences, in Cartesian coordinates, was used. It transforms the system of partial differential equations into a system of ordinary equations, with the unknowns, the temperature and humidity of both the air and the textile material. The simulation results were compared with experimental data obtained from the literature. In the statistical analysis the Shapiro-Wilk test was used to validate the model and, in all cases simulated, the results were p-values greater than 5 %, indicating normality of the data. The R-squared values were above 0.997 and the ratios Fcalculated/Fsimulated, at the 95 % confidence level, higher than five, indicating that the modeling was predictive in all simulations.

with measurements in the boundary layer flow around a heated vertical slender cylinder in a full-scale test room with displacement ventilation. Both velocity and temperature profiles in the boundary layer flow were recorded. The room was ventilated by a low velocity diffuser, standing on the floor, from which air......The equations, based on an integral formulation, for turbulent natural boundary layer flow are solved in both the constant temperature case and in the constant heat flux case. Solutions are found. for convection along both flat plates and cylinders. Theoretical predictions are compared...... with a negative buoyancy was supplied. The vertical distribution of both temperature and contamination in the room was measured as a function of the heat load and the air flow rate. The contaminant distribution showed a clear stratification between clean and contaminated air, while the temperature was increasing...

The separation of fission products from liquid solutions using centrifugal forces may prove an effective alternative to chemical processing in cases where radioactive materials necessitate minimal mixed-waste products or when allowing access to sophisticated chemical processing is undesirable. This investigation is a part of the effort to establish the feasibility of using liquid centrifugation for nuclear waste separation in the Accelerator Driven Energy Production (ADEP) program. A number of fundatmental issues in liquid centrifugation with radioactive elements need to be addressed in order to validate the approach and provide design criteria for experimental liquid salt (LiF and BeF{sub 2}) centrifuge. The author concentrates on one such issue, the possible onset of convective instabilities which could inhibit separation.

Solar PV (photovoltaic) is a rapidly advancing renewable energy technology which converts sunlight directly into electricity. One of the outstanding challenges of the current PV technology is the reduction in its conversion efficiency with increasing PV panel temperature, which is closely associated with the increase in solar intensity and the ambient temperature surrounding the PV panels. To more effectively capture the available energy when the sun is most intense, significant efforts have been invested in active and passive cooling research over the last few years. While integrated cooling systems can lead to the highest total efficiencies, they are usually neither the most feasible nor the most cost effective solutions. This work examines some simple passive means of manipulating the prevailing wind turbulence to enhance convective heat transfer over a heated plate in a wind tunnel.

Spherical shells used as laser targets in inertial confinement fusion (ICF) experiments are made by micro-encapsulation. In one phase of manufacturing, the spherical shells contain a solvent (fluoro-benzene, FB) and a solute (polystyrene, PAMS) in a water-FB environment. Evaporation of the FB results in the desired hardened plastic hollow spherical shells, 1-2 mm in diameter. Perfect sphericity is demanded for efficient fusion ignition and the observed surface roughness maybe driven by Marangoni instabilities due to surface tension dependence on the FB concentration (buoyant forces are negligible in this micro-scale problem). Here we model this drying process and compute nonlinear, time-dependent, axisymmetric, variable viscosity, infinite Schmidt number soluto-capillary convection in the shells. Comparison with results from linear theory and available experiments are made. (authors)

Recent observations and models have raised questions about our understanding of the dynamics of the deep solar convection. In particular, the amplitude of low wavenumber convective motions appears to be too high in both local area radiative magnetohydrodynamic and global spherical shell magnetohydrodynamic simulations. In global simulations this results in weaker than needed rotational constraints and consequent non solar-like differential rotation profiles. In deep local area simulations it yields strong horizontal flows in the photosphere on scales much larger than the observed supergranulation. We have undertaken numerical studies that suggest that solution to this problem is closely related to the long standing question of the origin of the solar supergranulation. Two possibilities have emerged. One suggests that small scale photospherically driven motions dominate convecive transport even at depth, descending through a very nearly adiabatic interior (more more nearly adiabatic than current convection models achieve). Convection of this form can meet Rossby number constraints set by global scale motions and implies that the solar supergranulation is the largest buoyantly driven scale of motion in the Sun. The other possibility is that large scale convection driven deeep in the Sun dynamically couples to the near surface shear layer, perhaps as its origin. In this case supergranulation would be the largest non-coupled convective mode, or only weakly coupled and thus potentially explaining the observed excess power in the prograde direction. Recent helioseismic results lend some support to this. We examind both of these possibilities using carefully designed numerical experiments, and weigh thier plausibilities in light of recent observations.

There is a need for innovative educational experiences that unify and reinforce fundamental principles at the interface between the physical, chemical, and life sciences. These experiences empower and excite students by helping them recognize how interdisciplinary knowledge can be applied to develop new products and technologies that benefit society. Microfluidics offers an incredibly versatile tool to address this need. Here we describe our efforts to create innovative hands-on activities that introduce chemical engineering students to molecular biology by challenging them to harness microscale natural convection phenomena to perform DNA replication via the polymerase chain reaction (PCR). Experimentally, we have constructed convective PCR stations incorporating a simple design for loading and mounting cylindrical microfluidic reactors between independently controlled thermal plates. A portable motion analysis microscope enables flow patterns inside the convective reactors to be directly visualized using fluorescent bead tracers. We have also developed a hands-on computational fluid dynamics (CFD) exercise based on modeling microscale thermal convection to identify optimal geometries for DNA replication. A cognitive assessment reveals that these activities strongly impact student learning in a positive way.

Convective cells are excited externally in a fully ionized magnetized plasma and their space-time evolution is investigated by two-dimensional potential measurements. A positive cell is excited externally by control of the end losses in the 'scrape off' layer of a plasma column produced by surface...

Presents development of systematic studies for hydrodynamics and heat and mass transfer in laminar free convection, accelerating film boiling and condensation of Newtonian fluids, and accelerating film flow of non-Newtonian power-law fluids. This book provides a system of analysis models with a developed velocity component method.

We study penetrative convection of a fluid confined between two horizontal plates, the temperatures of which are such that a temperature of maximum density lies between them. The range of Rayleigh numbers studied is Ra=[0.01 ,4 ]106,108 and the Prandtl numbers are Pr=1 and 11.6. An evolution equation for the growth of the convecting region is obtained through an integral energy balance. We identify a new nondimensional parameter, Λ , which is the ratio of temperature difference between the stable and unstable regions of the flow; larger values of Λ denote increased stability of the upper stable layer. We study the effects of Λ on the flow field using well-resolved lattice Boltzmann simulations and show that the characteristics of the flow depend sensitively upon it. For the range Λ = , we find that for a fixed Ra the Nusselt number, Nu, increases with decreasing Λ . We also investigate the effects of Λ on the vertical variation of convective heat flux and the Brunt-Väisälä frequency. Our results clearly indicate that in the limit Λ →0 the problem reduces to that of the classical Rayleigh-Bénard convection.

RCEMIP, an intercomparison of multiple types of models configured in radiative-convective equilibrium (RCE), is proposed. RCE is an idealization of the climate system in which there is a balance between radiative cooling of the atmosphere and heating by convection. The scientific objectives of RCEMIP are three-fold. First, clouds and climate sensitivity will be investigated in the RCE setting. This includes determining how cloud fraction changes with warming and the role of self-aggregation of convection in climate sensitivity. Second, RCEMIP will quantify the dependence of the degree of convective aggregation and tropical circulation regimes on temperature. Finally, by providing a common baseline, RCEMIP will allow the robustness of the RCE state across the spectrum of models to be assessed, which is essential for interpreting the results found regarding clouds, climate sensitivity, and aggregation, and more generally, determining which features of tropical climate a RCE framework is useful for. A novel aspect and major advantage of RCEMIP is the accessibility of the RCE framework to a variety of models, including cloud-resolving models, general circulation models, global cloud-resolving models, single-column models, and large-eddy simulation models.

The vortices emerging in rotating turbulent Rayleigh-Bénard convection in water at Rayleigh number Ra=6.0×108 are investigated using stereoscopic particle image velocimetry and by direct numerical simulation. The so-called Q criterion is used to detect the vortices from velocity fields. This

Full Text Available Closure is a problem of defining the convective intensity in a given parameterization. In spite of many years of efforts and progress, it is still considered an overall unresolved problem. The present article reviews this problem from phenomenological perspectives. The physical variables that may contribute in defining the convective intensity are listed, and their statistical significances identified by observational data analyses are reviewed. A possibility is discussed for identifying a correct closure hypothesis by performing a linear stability analysis of tropical convectively coupled waves with various different closure hypotheses. Various individual theoretical issues are considered from various different perspectives. The review also emphasizes that the dominant physical factors controlling convection differ between the tropics and extra-tropics, as well as between oceanic and land areas. Both observational as well as theoretical analyses, often focused on the tropics, do not necessarily lead to conclusions consistent with our operational experiences focused on midlatitudes. Though we emphasize the importance of the interplays between these observational, theoretical and operational perspectives, we also face challenges for establishing a solid research framework that is universally applicable. An energy cycle framework is suggested as such a candidate.

We have performed laboratory experiments in a aspect ratio Γ = 2 cylinder using liquid gallium (Pr = 0 . 023) as the working fluid. The Ekman number varies from E = 4 ×10-5 to 4 ×10-6 and the Rayleigh number varies from Ra = 3 ×105 to 2 ×107 . Using heat transfer and temperature measurements within the fluid, we characterize the different styles of low Pr rotating convective flow. The convection threshold is first overcome in the form of a container scale inertial oscillatory mode. At stronger forcing, wall-localized modes develop, coexisting with the inertial oscillatory modes in the bulk. When the strength of the buoyancy increases further, the bulk flow becomes turbulent while the wall modes remain. Our results imply that rotating convective flows in liquid metals do not develop in the form of quasi-steady columns, as in Pr = 1 planetary and stellar dynamo models, but in the form of oscillatory motions. Therefore, convection driven dynamo action in low Pr fluids can differ substantively than that occurring in typical Pr = 1 numerical models. Our results also suggest that low wavenumber, wall modes may be dynamically and observationally important in liquid metal dynamo systems. We thank the NSF Geophysics Program for support of this project.

Presents an undergraduate laboratory experiment in which a solar collector is used to heat water for domestic use. The working fluid is moved by natural convection so no pumps are required. Experimental apparatus is simple in design and operation so that data can be collected quickly and easily. (Author/JN)

In this paper the cooling of a low-heat-resistance sheet that moves downwards is considered. The free-convective velocities are assumed to be much larger than the velocity of the sheet. As a result the motion of the fluid is mainly towards the point where the sheet enters the system and a ‘backward’

Natural convection flow induced by heating from below in a irregular porous cavity is investigated numerically. The influence of the modified Rayleigh number and geometric ratios on heat transfer and fluid flow is studied. Global and local Nusselt for Rayleigh numbers covering the range 0 - 1600 and for several geometric ratios. The fluid flow and the temperature field are illustrated by contour maps. (author)

Three-dimensional numerical simulations of compressible turbulent thermally driven convection, in both slab and spheroidal geometries, are reviewed and analyzed in terms of velocity spectra and mixing-length theory. The same ideal gas model is used in both geometries, and resulting flows are compared. The piecewise-parabolic method (PPM), with either thermal conductivity or photospheric boundary conditions, is used to solve the fluid equations of motion. Fluid motions in both geometries exhibit a Kolmogorov-like k(sup -5/3) range in their velocity spectra. The longest wavelength modes are energetically dominant in both geometries, typically leading to one convection cell dominating the flow. In spheroidal geometry, a dipolar flow dominates the largest scale convective motions. Downflows are intensely turbulent and up drafts are relatively laminar in both geometries. In slab geometry, correlations between temperature and velocity fluctuations, which lead to the enthalpy flux, are fairly independent of depth. In spheroidal geometry this same correlation increases linearly with radius over the inner 70 percent by radius, in which the local pressure scale heights are a sizable fraction of the radius. The effects from the impenetrable boundary conditions in the slab geometry models are confused with the effects from non-local convection. In spheroidal geometry nonlocal effects, due to coherent plumes, are seen as far as several pressure scale heights from the lower boundary and are clearly distinguishable from boundary effects.

We propose to perform turbulent flow simulations in such manner that the difference operators do have the same symmetry properties as the corresponding differential operators. That is, the convective operator is represented by a skew-symmetric difference operator and the diffusive operator is

A discussion of the fundamental differences between laboratory convection in a stellar atmosphere is presented. The shortcomings of laterally homogeneous model atmospheres are analysed, and the extent to which these shortcoming are avoided in the two-component representation is discussed. Finally a qualitative discussion on the scaling properties of stellar granulation is presented. (Auth.)

Heat convection in thin cylinders and analysis about natural convection for straight vertical plates, and straight vertical cylinders submersed in a fluid are presented some works carry out by different authors in the field of heat transfer. In the part of conduction, deduction of the equation of heat conduction in cylindrical coordinates by means of energy balance in a control volume is presented. Enthalpy and internal energy are used for the outlining of the equation and finally the equation in its vectorial form is obtained. In the convection part development to calculate the Nusselt number for a straight vertical plate by a forces analysis, an energy balance and mass conservation over a control volume is outlined. Several empiric correlations to calculate the Nusselt number and its relations with other dimensionless numbers are presented. In the experimental part the way in which a prototype rode is assembled is presented measurements of temperatures attained in steady state and in free convection for working fluids as air and water are showed in tables. Also graphs of Nusselt numbers obtained in the experimental way through some empiric correlations are showed (Author)

Particle filters have been developed in recent years to deal with highly nonlinear dynamics and non Gaussian error statistics that also characterize data assimilation on convective scales. In this work we explore the use of the efficient particle filter (P.v. Leeuwen, 2011) for convective scale data assimilation application. The method is tested in idealized setting, on two stochastic models. The models were designed to reproduce some of the properties of convection, for example the rapid development and decay of convective clouds. The first model is a simple one-dimensional, discrete state birth-death model of clouds (Craig and Würsch, 2012). For this model, the efficient particle filter that includes nudging the variables shows significant improvement compared to Ensemble Kalman Filter and Sequential Importance Resampling (SIR) particle filter. The success of the combination of nudging and resampling, measured as RMS error with respect to the 'true state', is proportional to the nudging intensity. Significantly, even a very weak nudging intensity brings notable improvement over SIR. The second model is a modified version of a stochastic shallow water model (Würsch and Craig 2013), which contains more realistic dynamical characteristics of convective scale phenomena. Using the efficient particle filter and different combination of observations of the three field variables (wind, water 'height' and rain) allows the particle filter to be evaluated in comparison to a regime where only nudging is used. Sensitivity to the properties of the model error covariance is also considered. Finally, criteria are identified under which the efficient particle filter outperforms nudging alone. References: Craig, G. C. and M. Würsch, 2012: The impact of localization and observation averaging for convective-scale data assimilation in a simple stochastic model. Q. J. R. Meteorol. Soc.,139, 515-523. Van Leeuwen, P. J., 2011: Efficient non-linear data assimilation in geophysical

The international symposium on convective heat transfer was held on 19-23 August 1996, in Cesme, Izmir, Turkey. The spesialists discussed forced convection, heat exchangers, free convection and multiphase media and phase change at the meeting. Almost 53 papers were presented in the meeting

Transport of solutes through brain involves diffusion and convection. The importance of convective flow in the subarachnoid and paravascular spaces has long been recognized; a recently proposed 'glymphatic' clearance mechanism additionally suggests that aquaporin-4 (AQP4) water channels facilitate convective transport through brain parenchyma. Here, the major experimental underpinnings of the glymphatic mechanism were re-examined by measurements of solute movement in mouse brain following intracisternal or intraparenchymal solute injection. We found that: (i) transport of fluorescent dextrans in brain parenchyma depended on dextran size in a manner consistent with diffusive rather than convective transport; (ii) transport of dextrans in the parenchymal extracellular space, measured by 2-photon fluorescence recovery after photobleaching, was not affected just after cardiorespiratory arrest; and (iii) Aqp4 gene deletion did not impair transport of fluorescent solutes from sub-arachnoid space to brain in mice or rats. Our results do not support the proposed glymphatic mechanism of convectivesolute transport in brain parenchyma.

Entropy analysis in a mixed convection Poiseulle flow of a Molybdenum Disulphide Jeffrey Nanofluid (MDJN) is presented. Mixed convection is caused due to buoyancy force and external pressure gradient. The problem is formulated in terms of a boundary value problem for a system of partial differential equations. An analytical solution for the velocity and the temperature is obtained using the perturbation technique. Entropy generation has been derived as a function of the velocity and temperature gradients. The solutions are displayed graphically and the relevant importance of the input parameters is discussed. A Jeffrey nanofluid (JN) has been compared with a second grade nanofluid (SGN) and Newtonian nanofluid (NN). It is found that the entropy generation decreases when the temperature increases whereas increasing the Brickman number increases entropy generation.

In this paper, the free convective flow of magnetohydrodynamic fluid through a channel with time periodic boundary condition is investigated by taking the effects of Joule dissipation into consideration. Based on simplifying assumptions, the coupled governing equations are reduced to a set of nonlinear boundary valued problem. Approximate solutions are obtained by using semi-analytical Adomian decomposition method. The effect of pertinent parameters on the fluid velocity, temperature distribution, Nusselt number and skin friction are presented graphically and discussed. The result of the computation shows that an increase in the magnetic field intensity has significant influence on the fluid flow. - Highlights: • The influence of magnetic field on the free convective fluid flow is considered. • The coupled equations are solved by using Adomian decomposition method. • The Adomian series solution agreed with previously obtained result. • Magnetic field decreases the velocity maximum but enhances temperature field

Theoretical solutions of forced convection film boiling heat transfer from horizontal cylinders in saturated liquids were obtained based on a two-phase laminar boundary layer film boiling model. It was clarified that author's experimental data for the cylinders with the nondimensional diameters, D, of around 1.3 in water and in Freon-113 agreed with the values of theoretical numerical solutions based on the two-phase laminar boundary layer model with the smooth vapor-liquid interface except those for low flow velocities. A forced convection film boiling heat transfer correlation including the radiation contribution from the cylinders with various diameters in saturated and subcooled liquids was developed based on the two-phase laminar boundary layer film boiling model and the experimental data for water and Freon-113 at wide ranges of flow velocities, surface superheats, system pressures and cylinder diameters. (author)

Melting and, conversely, solidification processes in the presence of convection are key to many geophysical problems. An essential question related to these phenomena concerns the estimation of the (time-evolving) melting rate, which is tightly connected to the turbulent convective dynamics in the bulk of the melt fluid and the heat transfer at the liquid-solid interface. In this work, we consider a convective-melting model, constructed as a generalization of the Rayleigh-Bénard system, accounting for the basal melting of a solid. As the change of phase proceeds, a fluid layer grows at the heated bottom of the system and eventually reaches a turbulent convection state. By means of extensive lattice-Boltzmann numerical simulations employing an enthalpy formulation of the governing equations, we explore the model dynamics in two- and three-dimensional configurations. The focus of the analysis is on the scaling of global quantities like the heat flux and the kinetic energy with the Rayleigh number, as well as on the interface morphology and the effects of space dimensionality. Independently of dimensionality, we find that the convective-melting system behavior shares strong resemblances with that of the Rayleigh-Bénard one, and that the heat flux is only weakly enhanced with respect to that case. Such similarities are understood, at least to some extent, considering the resulting slow motion of the melting front (with respect to the turbulent fluid velocity fluctuations) and its generally little roughness (compared to the height of the fluid layer). Varying the Stefan number, accounting for the thermodynamical properties of the material, also seems to have only a mild effect, which implies the possibility of extrapolating results in numerically delicate low-Stefan setups from more convenient high-Stefan ones. Finally, we discuss the implications of our findings for the geophysically relevant problem of modeling Arctic ice melt ponds.

This book presents recent developments in our systematic studies of hydrodynamics and heat and mass transfer in laminar free convection, accelerating film boiling and condensation of Newtonian fluids, as well as accelerating film flow of non-Newtonian power-law fluids (FFNF). These new developments provided in this book are (i) novel system of analysis models based on the developed New Similarity Analysis Method; (ii) a system of advanced methods for treatment of gas temperature- dependent physical properties, and liquid temperature- dependent physical properties; (iii) the organically combined models of the governing mathematical models with those on treatment model of variable physical properties; (iv) rigorous approach of overcoming a challenge on accurate solution of three-point boundary value problem related to two-phase film boiling and condensation; and (v) A pseudo-similarity method of dealing with thermal boundary layer of FFNF for greatly simplifies the heat-transfer analysis and numerical calculati...

dependencies. If we can demonstrate that convective rainfall would be enhanced through feasible agricultural and engineering methods, then land surface-based weather modification deserves serious consideration as a solution for water scarcity and anthropogenic climate change.

MHD natural convection in open cavity becomes very important in many scientific and engineering problems, because of it's application in the design of electronic devices, solar thermal receivers, uncovered flat plate solar collectors having rows of vertical strips, geothermal reservoirs, etc. Several experiments and numerical investigations have been presented for describing the phenomenon of natural convection in open cavity for two decades. MHD natural convection and fluid flow in a two-dimensional open inclined square cavity with a heated circular cylinder was considered. The opposite wall to the opening side of the cavity was first kept to constant heat flux q, at the same time the surrounding fluid interacting with the aperture was maintained to an ambient temperature T∞. The top and bottom wall was kept to low and high temperature respectively. The fluid with different Prandtl numbers. The properties of the fluid are assumed to be constant. As a result a buoyancy force is created inside the cavity due to temperature difference and natural convection is formed inside the cavity. The Computational Fluid Dynamics (CFD) code are used to discretize the solution domain and represent the numerical result to graphical form.. Triangular meshes are used to obtain the solution of the problem. The streamlines and isotherms are produced, heat transfer parameter Nu are obtained. The results are presented in graphical as well as tabular form. The results show that heat flux decreases for increasing inclination of the cavity and the heat flux is a increasing function of Prandtl number Pr and decreasing function of Hartmann number Ha. It is observed that fluid moves counterclockwise around the cylinder in the cavity. Various recirculations are formed around the cylinder. The almost all isotherm lines are concentrated at the right lower corner of the cavity. The object of this work is to develop a Mathematical model regarding the effect of MHD natural convection flow around

The free convection boundary layer flow with simultaneous heat and mass transfer in a porous medium is studied when the boundary wall moves in its own plane with suction. The study also incorporates chemical reaction for the very simple model of a binary reaction with Arrhenius activation energy. For large suction asymptotic approximate solutions are obtained for the flow variables for various values of the activation energy. (author). 10 refs, 2 figs

Full Text Available The objective of this study is to explore the influence of wall slip condition on a free convection flow of an incompressible viscous fluid with heat transfer and ramped wall temperature. Exact solution of the problem is obtained by using Laplace transform technique. Graphical results to see the effects of Prandtl number Pr, time t, and slip parameter η on velocity and skin friction for the case of ramped and constant temperature of the plate are provided and discussed.

An unsteady viscous incompressible free convection flow of an electrically conducting fluid between two heated vertical parallel plates is considered in presence of a uniform magnetic field applied transversely to the flow. The approximate analytical solutions for velocity, induced field and temperature distributions are obtained for small and large magnetic Reynolds number. The skin-friction on the two plates are obtained and plotted graphically. The problem is extended for thermometric case. (author)

Full Text Available An analytic (series solution is developed to describe the thermal performance of a porous radial fin with natural convection in the fluid saturating the fin and radiation heat loss from the top and bottom surfaces of the fin. The HAM results for the temperature distribution and base heat flux are compared with the direct numerical results and found to be very accurate.

Full Text Available The problem of steady, laminar, thermal Marangoni convection flow of non-Newtonian power law fluid along a horizontal surface with variable surface temperature is studied. The partial differential equations are transformed into ordinary differential equations by using a suitable similarity transformation and analytical approximate solutions are obtained by an efficient transformation, asymptotic expansion and Padé approximants technique. The effects of power law index and Marangoni number on velocity and temperature profiles are examined and discussed.

A new and consistent convection scheme (PCMT: Prognostic Condensates Microphysics and Transport), providing a continuous and prognostic treatment of this atmospheric process, is described. The main concept ensuring the consistency of the whole system is the buoyancy, key element of any vertical motion. The buoyancy constitutes the forcing term of the convective vertical velocity, which is then used to define the triggering condition, the mass flux, and the rates of entrainment-detrainment. The buoyancy is also used in its vertically integrated form (CAPE) to determine the closure condition. The continuous treatment of convection, from dry thermals to deep precipitating convection, is achieved with the help of a continuous formulation of the entrainment-detrainment rates (depending on the convective vertical velocity) and of the CAPE relaxation time (depending on the convective over-turning time). The convective tendencies are directly expressed in terms of condensation and transport. Finally, the convective vertical velocity and condensates are fully prognostic, the latter being treated using the same microphysics scheme as for the resolved condensates but considering the convective environment. A Single Column Model (SCM) validation of this scheme is shown, allowing detailed comparisons with observed and explicitly simulated data. Four cases covering the convective spectrum are considered: over ocean, sensitivity to environmental moisture (S. Derbyshire) non precipitating shallow convection to deep precipitating convection, trade wind shallow convection (BOMEX) and strato-cumulus (FIRE), together with an entire continental diurnal cycle of convection (ARM). The emphasis is put on the characteristics of the scheme which enable a continuous treatment of convection. Then, a 3D LAM validation is presented considering an AMMA case with both observations and a CRM simulation using the same initial and lateral conditions as for the parameterized one. Finally, global

A means of determining the thermal responses of the core and the components of a high-temperature gas-cooled reactor after loss of forced coolant flow is discussed. A computer program, using a finite-difference technique, is presented together with a solution of the confined natural convection. The results obtained are reasonable and demonstrate that the computer program adequately represents the confined natural convection

We present and analyze a numerical method for the solution of a class of scalar, multi-dimensional, nonlinear degenerate convection-diffusion equations. The method is based on operator splitting to separate the convective and the diffusive terms in the governing equation. The nonlinear, convective part is solved using front tracking and dimensional splitting, while the nonlinear diffusion equation is solved by a suitable difference scheme. We verify L{sup 1} compactness of the corresponding set of approximate solutions and derive precise entropy estimates. In particular, these results allow us to pass to the limit in our approximations and recover an entropy solution of the problem in question. The theory presented covers a large class of equations. Important subclasses are hyperbolic conservation laws, porous medium type equations, two-phase reservoir flow equations, and strongly degenerate equations coming from the recent theory of sedimentation-consolidation processes. A thorough numerical investigation of the method analyzed in this paper (and similar methods) is presented in a companion paper. (author)

In this paper we investigate the properties of advection-dominated accretion flows(ADAFs) in case that outflows carry away infalling matter with its angular momentum and energy. Positive Bernoulli numbers in ADAFs allow a fraction of the gas to be ex-pelled in a form of outflows. The ADAFs are also unstable to convection. We present self-similar solutions for advection-dominated accretion flows in the presence of out-flows from the accretion flows (ADIOS). The axisymmetric flow is treated in variables integrated over polar sections and the effects of outflows on the accretion rlow are parameterized for possible configurations compatible with the one dimensional self-similar ADAF solution. We explicitly derive self-similar solutions of ADAFs in the presence of outflows and show that the strong outflows in the accretion flows result in a flatter density profile, which is similar to that of the convection-dominated accretion flows (CDAFs) in which convection transports the a! ngular momentum inward and the energy outward. These two different versions of the ADAF model should show similar behaviors in X-ray spectrum to some extent. Even though the two models may show similar behaviors, they should be distinguishable due to different physical properties. We suggest that for a central object of which mass is known these two different accretion flows should have different X-ray flux value due to deficient matter in the wind model.

Full Text Available In this paper we investigate the properties of advection-dominated accretion flows(ADAFs in case that outflows carry away infalling matter with its angular momentum and energy. Positive Bernoulli numbers in ADAFs allow a fraction of the gas to be ex-pelled in a form of outflows. The ADAFs are also unstable to convection. We present self-similar solutions for advection-dominated accretion flows in the presence of out-flows from the accretion flows (ADIOS. The axisymmetric flow is treated in variables integrated over polar sections and the effects of outflows on the accretion rlow are parameterized for possible configurations compatible with the one dimensional self-similar ADAF solution. We explicitly derive self-similar solutions of ADAFs in the presence of outflows and show that the strong outflows in the accretion flows result in a flatter density profile, which is similar to that of the convection-dominated accretion flows (CDAFs in which convection transports the a! ngular momentum inward and the energy outward. These two different versions of the ADAF model should show similar behaviors in X-ray spectrum to some extent. Even though the two models may show similar behaviors, they should be distinguishable due to different physical properties. We suggest that for a central object of which mass is known these two different accretion flows should have different X-ray flux value due to deficient matter in the wind model.

Successfully forecasting when and where individual convective storms will form remains an elusive goal for short-term numerical weather prediction. In this dissertation, the convective initiation (CI) challenge is considered as a problem of insufficiently resolved initial conditions and dense surface weather observations are explored as a possible solution. To better quantify convective-scale surface variability in numerical simulations of discrete convective initiation, idealized ensemble simulations of a variety of environments where CI occurs in response to boundary-layer processes are examined. Coherent features 1-2 hours prior to CI are found in all surface fields examined. While some features were broadly expected, such as positive temperature anomalies and convergent winds, negative temperature anomalies due to cloud shadowing are the largest surface anomaly seen prior to CI. Based on these simulations, several hypotheses about the required characteristics of a surface observing network to constrain CI forecasts are developed. Principally, these suggest that observation spacings of less than 4---5 km would be required, based on correlation length scales. Furthermore, it is anticipated that 2-m temperature and 10-m wind observations would likely be more relevant for effectively constraining variability than surface pressure or 2-m moisture observations based on the magnitudes of observed anomalies relative to observation error. These hypotheses are tested with a series of observing system simulation experiments (OSSEs) using a single CI-capable environment. The OSSE results largely confirm the hypotheses, and with 4-km and particularly 1-km surface observation spacing, skillful forecasts of CI are possible, but only within two hours of CI time. Several facets of convective-scale assimilation, including the need for properly-calibrated localization and problems from non-Gaussian ensemble estimates of the cloud field are discussed. Finally, the characteristics

A modification of Ivantsov's (1947) similarity solutions is proposed which can describe phase-change processes which are limited by diffusion. The method has application to systems that have n-components and possess cross-diffusion and Soret and Dufour effects, along with convection driven by density discontinuities at the two-phase interface. Local thermal equilibrium is assumed at the interface. It is shown that analytic solutions are possible when the material properties are constant.

The generation of magnetic fields in planetary and stellar interiors are believed to be controlled primarily by turbulent convection constrained by Coriolis and Lorentz forces in their electrically conducting fluid layers. Yet relatively few laboratory experiments are capable of investigating the different regimes of turbulent magnetohydrodynamic convection. In this work, we perform one laboratory experiment in a cylinder at a fixed heat flux using the liquid metal gallium in order to investigate, sequentially: Rayleigh-Bènard convection without any imposed constraints, magnetoconvection with a Lorentz constraint imposed by vertical magnetic field, rotating convection with a Coriolis constraint imposed by rotation, and finally the magnetostrophic convective regime where both Coriolis and Lorentz are imposed and equal. Using an array of internal and external temperature probes, we show that each regime along the path to magnetostrophic convection is unique. The behaviors and transitions in the dominant modes of convection as well as their fundamental frequencies and wavenumbers are investigated.

In high β stellarator and tokamak reactors, the plasma pressure gradient in some regions of the plasma may exceed the critical pressure gradient set by ballooning instabilities. In these regions, convective cells break out to enhance the transport. As a result, the pressure gradient can rise only slightly above the critical gradient and the plasma is in another state of equilibrium - ''convective equilibrium'' - in these regions. Although the convective transport cannot be calculated precisely, it is shown that the density and temperature profiles in the convective region can still be estimated. A simple mixing-length theory, similar to that used for convection in stellar interiors, is introduced in this paper to provide a qualitative description of the convective cells and to show that the convective transport is highly efficient. A numerical example for obtaining the density and temperature profiles in a stellarator reactor is given

Full Text Available Natural convection in horizontal annular porous media has become a subject receiving increasing attention due to its practical importance in the problem of insulators, such as ducting system in high temperature gas-cooled reactors, heating systems, thermal energy storage systems, under ground cable systems, etc. This paper presents a numerical study for steady state thermal convection in a fully saturated porous media bounded by two horizontal concentric cylinders, the cylinders are impermeable to fluid motion and maintained at different, uniform temperatures. The solution scheme is based on two-dimensional model, which is governed by Darcy-Oberbeck-Boussinesq equations. The finite element method using Galerkin technique is developed and employed to solve the present problem. A numerical simulation is carried out to examine the parametric effects of Rayleigh number and radius ratio on the role played by natural convection heat transfer in the porous annuli. The numerical results obtained from the present model were compared with the available published results and good agreement is observed. The average Nusselt number at the heating surface of the inner cylinder is correlated to Rayleigh number and radius ratio.Keywords: Natural convection, numerical investigation, saturated porous media, finite element method, concentric horizontal annuli.

Experimental results by Koster who studied natural convection processes in slender Hele-Shaw cells are simulated with an existing two-dimensional natural convection code. This investigation yields the following results: The basic model of the calculations, which assumes a constant temperature across the gap (smallest extent of the Hele-Shaw cell) and thus without heat exchange with the Plexiglas windows, leads to an underestimation of the experimentally obtained critical Rayleigh numbers (onset of convection, onset of oscillatory convection) by one order of magnitude and an overestimation of the nondimensional period compared to experimental findings. Another version of the code, which permits heat exchange with the windows reveals an overestimation of the critical Rayleigh numbers and smaller dimensionless periods than the experiments. By these two different approaches a twoside bounding the Koster's experiments are achieved. As the modified version overestimates the real heat transfer from and to the windows it may be concluded that using a suitably adapted heat transfer coefficient for the thermal coupling of the fluid and the windows numerical simulation would also reproduce quantitatively the results of Koster. The reason for the break down of the steady flow solution and the onset of transient flow was studied numerically by examining a model proposed by Howard. At this time no really satisfying answer to this question is available. (orig./GL) [de

Mixed convection flow in enclosures has been a subject of interest for many years due to their ever increasing applications in solar collectors, electronic cooling, lubrication technologies, food processing, and nuclear reactors. In comparison, little effort has been given to the problem of mixed convection in enclosures filled with nanofluids, while the addition of nanoparticles in a fluid base to alter specific material properties is considered a feasible solution for many heat transfer problems. Mixed convection of nanofluids is a challenging problem as the addition of nanoparticles changes the fluid’s thermo-physical properties as well as due to the complex interactions among inertia, viscous, and buoyancy forces. In this study, a two-dimensional steady-state numerical model has been developed to investigate mixed convection flow of nanofluids in a square enclosure with an intruded rectangular fin and to optimize the fin geometry for maximizing the heat transfer using the Constructal design. The model has been developed using ANSYS-FLUENT for various fin geometries. Flow fields, temperature fields, and heat transfer rates are examined for different values of Rayleigh and Reynolds numbers for several geometries of the fin with the aim of maximizing the heat transfer from the fin to the surrounding flow. Outcome of this study provides important insight into the heat transfer behavior of nanofluids, which will help in developing novel geometries with enhanced and controlled heat transfer for solar collectors and electronic devices.

The diffuse boundary layer between miscible liquids is subject to Rayleigh-Taylor instabilities if the heavy fluid is supported by the light one. The resulting rapid interchange of the liquids can be suppressed by enforcing vertical oscillations on the whole system. This dynamic stabilization is incomplete and produces some peculiar novel transport phenomena such as decay off the density profile into several steps, periodic peeling of density sheets of the boundary layer and the appearance of steady vortex flow. The theory presented in this paper identifies the basic mechanism as formation of convective cells leading to enhanced diffusion, and explains previous experimental results with water and ZnJ 2 -solutions. A nonlinear treatment of the stationary convective flow problem gives the saturation amplitude of the ground mode and provides an upper bound for the maximum convective transport. The hydrodynamic model can be used for visualizing similar transport processes in the plasma of toroidal confinement devices such as sawtooth oscillations in soft disruptions of tokamak discharges and anomalous diffusion by excitation of convective cells. The latter process is investigated here in some detail, leading to the result that the maximum possible transport is of the order of Bohm diffusion. (orig.)

Mixed convection flow in enclosures has been a subject of interest for many years due to their ever increasing applications in solar collectors, electronic cooling, lubrication technologies, food processing, and nuclear reactors. In comparison, little effort has been given to the problem of mixed convection in enclosures filled with nanofluids, while the addition of nanoparticles in a fluid base to alter specific material properties is considered a feasible solution for many heat transfer problems. Mixed convection of nanofluids is a challenging problem as the addition of nanoparticles changes the fluid’s thermo-physical properties as well as due to the complex interactions among inertia, viscous, and buoyancy forces. In this study, a two-dimensional steady-state numerical model has been developed to investigate mixed convection flow of nanofluids in a square enclosure with an intruded rectangular fin and to optimize the fin geometry for maximizing the heat transfer using the Constructal design. The model has been developed using ANSYS-FLUENT for various fin geometries. Flow fields, temperature fields, and heat transfer rates are examined for different values of Rayleigh and Reynolds numbers for several geometries of the fin with the aim of maximizing the heat transfer from the fin to the surrounding flow. Outcome of this study provides important insight into the heat transfer behavior of nanofluids, which will help in developing novel geometries with enhanced and controlled heat transfer for solar collectors and electronic devices.

Mixed convection flow in enclosures has been a subject of interest for many years due to their ever increasing applications in solar collectors, electronic cooling, lubrication technologies, food processing, and nuclear reactors. In comparison, little effort has been given to the problem of mixed convection in enclosures filled with nanofluids, while the addition of nanoparticles in a fluid base to alter specific material properties is considered a feasible solution for many heat transfer problems. Mixed convection of nanofluids is a challenging problem as the addition of nanoparticles changes the fluid's thermo-physical properties as well as due to the complex interactions among inertia, viscous, and buoyancy forces. In this study, a two-dimensional steady-state numerical model has been developed to investigate mixed convection flow of nanofluids in a square enclosure with an intruded rectangular fin and to optimize the fin geometry for maximizing the heat transfer using the Constructal design. The model has been developed using ANSYS-FLUENT for various fin geometries. Flow fields, temperature fields, and heat transfer rates are examined for different values of Rayleigh and Reynolds numbers for several geometries of the fin with the aim of maximizing the heat transfer from the fin to the surrounding flow. Outcome of this study provides important insight into the heat transfer behavior of nanofluids, which will help in developing novel geometries with enhanced and controlled heat transfer for solar collectors and electronic devices.

Constraining precipitation processes in climate models with observations is crucial to accurately simulating current climate and reducing uncertainties in future projections. Results from the Green Ocean Amazon (GOAmazon) field campaign (2014-2015) provide evidence that deep convection is strongly controlled by the availability of moisture in the free troposphere over the Amazon, much like over tropical oceans. Entraining plume buoyancy calculations confirm that CWV is a good proxy for the conditional instability of the environment, yet differences in convective onset as a function of CWV exist over land and ocean, as well as seasonally and diurnally over land. This is largely due to variability in the contribution of lower tropospheric humidity to the total column moisture. Boundary layer moisture shows a strong relationship to the onset during the day, which largely disappears during nighttime. Using S-Band radar, these transition statistics are examined separately for unorganized and mesoscale-organized convection, which exhibit sharp increases in probability of occurrence with increasing moisture throughout the column, particularly in the lower free troposphere. Retrievals of vertical velocity from a radar wind profiler indicate updraft velocity and mass flux increasing with height through the lower troposphere. A deep-inflow mixing scheme motivated by this — corresponding to deep inflow of environmental air into a plume that grows with height — provides a weighting of boundary layer and free tropospheric air that yields buoyancies consistent with the observed onset of deep convection across seasons and times of day, across land and ocean sites, and for all convection types. This provides a substantial improvement relative to more traditional constant mixing assumptions, and a dramatic improvement relative to no mixing. Furthermore, it provides relationships that are as strong or stronger for mesoscale-organized convection as for unorganized convection.

Full Text Available A correct representation of the coupling between convection and circulation constitutes a prerequisite for a correct representation of precipitation at all scales. In this study, the coupling between convection and a sea breeze is investigated across three main resolutions: large-eddy resolution where convection is fully explicit, convection-permitting resolution where convection is partly explicit and coarse resolution where convection is parameterised. The considered models are the UCLA-LES, COSMO and ICON. Despite the use of prescribed surface fluxes, comparison of the simulations reveals that typical biases associated with a misrepresentation of convection at convection-permitting and coarser resolutions significantly alter the characteristics of the sea breeze. The coarse-resolution simulations integrated without convective parameterisation and the convection-permitting simulations simulate a too slow propagation of the breeze front as compared to the large-eddy simulations. From the various factors affecting the propagation, a delayed onset and intensification of cold pools primarily explains the differences. This is a direct consequence of a delayed development of convection when the grid spacing is coarsened. Scaling the time the sea breeze reaches the centre of the land patch by the time precipitation exceeds 2 mm day−1, used as a measure for significant evaporation, yields a collapse of the simulations onto a simple linear relationship although subtle differences remain due to the use of different turbulence and microphysical schemes. Turning on the convection scheme significantly disrupts the propagation of the sea breeze due to a misrepresented timing (too early triggering and magnitude (too strong precipitation evaporation in one of the tested convection schemes of the convective processes.

Experimental and theoretical studies of convective heat transfer from a heat-generating fluid confined to a closed volume are reviewed. Theoretical results are inferred from analytical estimates based on the relevant conservation laws and the current understanding of the convective heat-transfer processes. Four basic and one asymptotic regime of heat transfer are identified depending on the heat generation rate. Limiting heat-transfer distribution patterns are found for the lower boundary. Heat transfer in a quasi-two-dimensional geometry is analyzed. Quasi-steady-state heat transfer from a cooling-down fluid without internal heat sources is studied separately. Experimental results and theoretical predictions are compared. (reviews of topical problems)

This paper demonstrates the application of the density-based topology optimisation approach for the design of heat sinks and micropumps based on natural convection effects. The problems are modelled under the assumptions of steady-state laminar flow using the incompressible Navier-Stokes equations...... coupled to the convection-diffusion equation through the Boussinesq approximation. In order to facilitate topology optimisation, the Brinkman approach is taken to penalise velocities inside the solid domain and the effective thermal conductivity is interpolated in order to accommodate differences...... in thermal conductivity of the solid and fluid phases. The governing equations are discretised using stabilised finite elements and topology optimisation is performed for two different problems using discrete adjoint sensitivity analysis. The study shows that topology optimisation is a viable approach...

Following Bandiera (1984), it is shown that the relevant criterion to determine the stability of a blast wave, propagating through the layers of a massive star in a supernova explosion, is the Schwarzschild (or Ledoux) criterion rather than the Rayleigh-Taylor criterion. Both criteria coincide only in the incompressible limit. Results of a linear stability analysis are presented for a one-dimensional (spherical) explosion in a realistic model for the progenitor of SN 1987A. When applying the Schwarzschild criterion, unstable regions get extended considerably. Convection is found to develop behind the shock, with a characteristic growth rate corresponding to a time scale much smaller than the shock traversal time. This ensures that efficient mixing will take place. Since the entire ejected mass is found to be convectively unstable, Ni can be transported outward, even into the hydrogen envelope, while hydrogen can be mixed deep into the helium core.

A loss-of-coolant accident (LOCA) results in core melt formation and relocation at various locations within the reactor core over a considerable period of time. If there is no effective cooling mechanism, the core debris may heat up and commence natural circulation. The high temperature pool of molten core material will threaten the structural integrity of the reactor vessel. The extent and urgency of this threat depend primarily upon the intensity of the internal heat sources and upon the consequent distribution of the heat fluxes on the vessel walls in contact with the molten core material pools. In such a steady molten pool convection state, the thermal loads against the vessel would be determined by the in-vessel heat transfer distribution involving convective and conductive heat transfer from the decay-heated core material pool to the lower head wall in contact with the core material. In this study, upward and downward heat transfer fraction ratio is focused on

The aim of our study is to establish a reliable data base for improving thermal-hydraulic codes, in the field of turbulent flows with buoyancy forces. The flow considered is mixed convection in the Reynolds and Richardson number range: Re=10"3 to 6*10"4 and Ri=10"-"4 to 1. Experiments are carried out in an upward turbulent flow between vertical parallel plates at different wall temperatures. Part 1 gives a detailed data base of turbulent mixed flow of free and forced convection. Part II presents the installation and the calibration system intended for probes calibration. Part III describes the measurement technique (constant-temperature probe and cold-wire probe) and the method for measuring the position of the hot-wire anemometer from the wall surface. The measurement accuracy is within 0.001 mm in the present system. Part IV relates the development of a method for near wall measurements. This correction procedure for hot-wire anemometer close to wall has been derived on the basis of a two-dimensional numerical study. The method permits to obtain a quantitative correction of the wall influence on hot-wires and takes into account the velocity profile and the effects the wall material has on the heat loss. Part V presents the experimental data obtained in the channel in forced and mixed convection. Results obtained in the forced convection regime serve as a verification of the measurement technique close to the wall and give the conditions at the entrance of the test section. The effects of the buoyancy force on the mean velocity and temperature profiles are confirmed. The buoyancy strongly affects the flow structure and deforms the distribution of mean velocity. The velocity profiles are asymmetric. The second section of part V gives an approach of analytical wall functions with buoyancy forces, on the basis of the experimental data obtained in the test section. (author) [fr

It has been advocated that convective and crystal settling processes play significant, and perhaps crucial, roles in magmatic differentiation. The fluid dynamics of magma chambers have been extensively studied in recent years, both theoretically and experimentally, but there is disagreement over the nature and scale of the convection, over its bearing on fractionation and possibly over whether it occurs at all. The differential distribution of modal olivine with height in differentiated alkaline basic sills provides critical evidence to resolve this controversy, at least for small to medium-large magma chambers. Our own and others' published data for such sills show that, irrespective of overall olivine content, modal olivine contents tend to increase in a roughly symmetrical manner inwards from the upper and lower margins of the sill, i.e. the distribution patterns are more often approximately D-shaped rather than the classic S-shape generally ascribed to gravity settling. We concur with the majority of other authors that this is an original feature of the filling process which has survived more or less unchanged since emplacement. We therefore conclude that the magmas have not undergone turbulent convection and that gravity settling has usually played only a minor modifying role since the intrusion of these sills. We offer a possible explanation for the apparent contradiction between fluid dynamical theory and the petrological evidence by suggesting that such sills rarely fill by the rapid injection of a single pulse of magma. Rather, they form from a series of pulses or a continuous pulsed influx over a protracted interval during which marginal cooling severely limits the potential for thermal convection.

The nonlinear behavior of RR Lyrae pulsations is investigated using a state-of-the-art numerical technique solving the full time-dependent system of radiation hydrodynamics. Grey radiative transfer is included by a variable Eddington-factor method and we use the time-dependent turbulent convection model according to Kuhfuss (1986, A&A 160, 116) in the version of Wuchterl (1995, Comp. Phys. Comm. 89, 19). OPAL opacities extended by the Alexander molecule opacities at temperatures below 6000 K and an equation of state according to Wuchterl (1990, A&A 238, 83) close the system. The resulting nonlinear system is discretized on an adaptive mesh developed by Dorfi & Drury (1987, J. Comp. Phys. 69, 175), which is important to provide the necessary spatial resolution in critical regions like ionization zones and shock waves. Additionally, we employ a second order advection scheme, a time centered temporal discretizaton and an artificial tensor viscosity in order to treat discontinuities. We compute fundamental as well first overtone models of RR Lyrae stars for a grid of stellar parameters both with and without convective energy transport in order to give a detailed picture of the pulsation-convection interaction. In order to investigate the influence of the different features of the convection model calculations with and without overshooting, turbulent pressure and turbulent viscosity are performed and compared with each other. A standard Fourier decomposition is used to confront the resulting light and radial velocity variations with recent observations and we show that the well known RR Lyrae phase discrepancy problem (Simon 1985, ApJ 299, 723) can be resolved with these stellar pulsation computations.

This article is concerned with natural convective heat transfer from square cylinder mounted on a plane adiabatic base, the cylinders having an exposed cylinder surface according to different horizontal angle. The cylinder receives heat from a radiating heater which results in a buoyant flow. There are many industrial applications, including refrigeration, ventilation and the cooling of electrical components, for which the present study may be applicable.

The mixed convection phenomena in the sodium pool of fast reactor have been studied systematically by the two dimensional modeling method. A generalized concept of circumferential line in the cylindrical coordinates was proposed to overcome the three dimensional effect induced by the pool geometry in an analysis of two dimensional modeling. A method of sub-step in time was developed for solving the turbulent equations. The treatments on the boundary condition for the auxiliary velocity field have been proposed, and the explanation of allowing the flow function method to be used in the flow field in presence of a mass source term was given. As examples of verification, the experiments were conducted with water flow in a rectangular cavity. The results from theoretical analysis were applied to the numerical computation for the mixed convection in the cavity. The mechanism of stratified flow in the cavity was studied. A numerical calculation was carried out for the mixed convection in hot plenum of a typical fast reactor

Boiling is an extremely effective way to promote heat transfer from a hot surface to a liquid due to numerous mechanisms, many of which are not understood in quantitative detail. An important component of the overall process is that the buoyancy of the bubble compounds with that of the liquid to give rise to a much-enhanced natural convection. In this article, we focus specifically on this enhancement and present a numerical study of the resulting two-phase Rayleigh-Bénard convection process in a cylindrical cell with a diameter equal to its height. We make no attempt to model other aspects of the boiling process such as bubble nucleation and detachment. The cell base and top are held at temperatures above and below the boiling point of the liquid, respectively. By keeping this difference constant, we study the effect of the liquid superheat in a Rayleigh number range that, in the absence of boiling, would be between 2 × 10(6) and 5 × 10(9). We find a considerable enhancement of the heat transfer and study its dependence on the number of bubbles, the degree of superheat of the hot cell bottom, and the Rayleigh number. The increased buoyancy provided by the bubbles leads to more energetic hot plumes detaching from the cell bottom, and the strength of the circulation in the cell is significantly increased. Our results are in general agreement with recent experiments on boiling Rayleigh-Bénard convection.

Most methods for modeling mantle convection in a two-dimensional (2D) circular annular domain suffer from innate shortcomings in their ability to capture several characteristics of the spherical shell geometry of planetary mantles. While methods such as rescaling the inner and outer radius to reduce anomalous effects in a 2D polar cylindrical coordinate system have been introduced and widely implemented, such fixes may have other drawbacks that adversely affect the outcome of some kinds of mantle convection studies. Here we propose a new approach that we term the "spherical annulus," which is a 2D slice that bisects the spherical shell and is quantitatively formulated at the equator of a spherical polar coordinate system after neglecting terms in the governing equations related to variations in latitude. Spherical scaling is retained in this approximation since the Jacobian function remains proportional to the square of the radius. We present example calculations to show that the behavior of convection in the spherical annulus compares favorably against calculations performed in other 2D annular domains when measured relative to those in a fully three-dimensional (3D) spherical shell.

Free convection, or fluid motion driven by density differences, is an important groundwater flow mechanism that can enhance transport and mixing of heat and solutes in the subsurface. Various issues of environmental and societal relevance are exacerbated convective mixing; it has been studied in the context of dense contaminant plumes, nuclear waste disposal, greenhouse gas sequestration, the impacts of sea level rise and saline intrusion on drinking water resources. The basic theory behind convective flow in porous media is well understood, but important questions regarding this process in natural systems remain unanswered. Most previous research on this topic has focused on theory and modeling, with only limited attention to experimental studies and field measurements. The few published studies present single snapshots, making it difficult to quantify transient changes in these systems. Non-invasive electrical methods have the potential to exploit the relation between solute concentrations and electrical conductance of a fluid, and thereby estimate fluid salinity differences in time and space. We present the results of a two-year experimental study at a shallow sabkha aquifer in the United Arab Emirates, about 50 km southwest of the city of Abu Dhabi along the coast of the Arabian Gulf, that was designed to explore the transient nature of free convection. Electrical resistivity tomography (ERT) data documented the presence of convective fingers following a significant rainfall event. One year later, the complex fingering pattern had completely disappeared. This observation is supported by analysis of the aquifer solute budget as well as hydrodynamic modeling of the system. The transient dynamics of the gravitational instabilities in the modeling results are in agreement with the timing observed in the time-lapse ERT data. Our experimental observations and modeling are consistent with the hypothesis that the instabilities arose from a dense brine that infiltrated

In this paper, the natural convective flow of nanofluids over a convectively heated vertical plate in a saturated Darcy porous medium is studied numerically. The governing equations are transformed into a set of ordinary differential equations by using appropriate similarity variables, and they are numerically solved using the fourth-order Runge-Kutta method associated with the Gauss-Newton method. The effects of parametric variation of the Brownian motion parameter (Nb), thermophoresis parameter (Nt) and the convective heating parameter (Nc) on the boundary layer profiles are investigated. Furthermore, the variation of the reduced Nusselt number and reduced Sherwood number, as important parameters of heat and mass transfer, as a function of the Brownian motion, thermophoresis and convective heating parameters is discussed in detail. The results show that the thickness of the concentration profiles is much lower than the temperature and velocity profiles. For low values of the convective heating parameter (Nc), as the Brownian motion parameter increases, the non-dimensional wall temperature increases. However, for high values of Nc, the effect of the Brownian motion parameter on the non-dimensional wall temperature is not significant. As the Brownian motion parameter increases, the reduced Sherwood number increases and the reduced Nusselt number decreases. (author)

Full Text Available In this study we test a stream function method suggested by Israelevich and Ershkovich for instantaneous reconstruction of global, high-latitude ionospheric convection patterns from a limited set of experimental observations, namely, from the electric field or ion drift velocity vector measurements taken along two polar satellite orbits only. These two satellite passes subdivide the polar cap into several adjacent areas. Measured electric fields or ion drifts can be considered as boundary conditions (together with the zero electric potential condition at the low-latitude boundary for those areas, and the entire ionospheric convection pattern can be reconstructed as a solution of the boundary value problem for the stream function without any preliminary information on ionospheric conductivities. In order to validate the stream function method, we utilized the IZMIRAN electrodynamic model (IZMEM recently calibrated by the DMSP ionospheric electrostatic potential observations. For the sake of simplicity, we took the modeled electric fields along the noon-midnight and dawn-dusk meridians as the boundary conditions. Then, the solution(s of the boundary value problem (i.e., a reconstructed potential distribution over the entire polar region is compared with the original IZMEM/DMSP electric potential distribution(s, as well as with the various cross cuts of the polar cap. It is found that reconstructed convection patterns are in good agreement with the original modelled patterns in both the northern and southern polar caps. The analysis is carried out for the winter and summer conditions, as well as for a number of configurations of the interplanetary magnetic field.

The problem of simultaneous heat and mass transfer in two-dimensional free convection from a semi-infinite vertical flat plate is investigated. An integral method is used to find a solution for zero wall velocity and for a mass transfer velocity at the wall with small-amplitude oscillatory wall temperature. Low and high-frequency solutions are developed separately and are discussed graphically with the effects of the parameters Gr (the Grashof number for heat transfer), Gc (the Grashof number for mass transfer) and Sc (the Schmidt number) for Pr=0.71 representing aid at 20 deg. C. (author)

A numerical study is made on the fully developed bifurcation structure of the forced convection in tightly coiled ducts of square cross-section. In addition to the examination of structural changes of three known solution branches found in loosely coiled ducts, three new solution branches are found. These new branches are isolated from the three known branches. The flows on these new branches are in a symmetric 4-cell state, a symmetric 8-cell state, an asymmetric 2-cell state, an asymmetric 5-cell state, an asymmetric 7-cell state, or an asymmetric 8-cell structure

Full Text Available The article presents modeling for investigation of aerodynamic processes on area sections (including a group of complex constructional works for different regimes of drop and wind streams and temperature conditions and in complex constructional works (for different regimes of heating and ventilation. There were developed different programs for innovation problems solution in the field of heat and mass exchange in three-dimensional space of pres- sures-speeds-temperatures of оbjects.The field of uses of pneumobasic objects: construction and roof of tennis courts, hockey pitches, swimming pools , and also exhibitions’ buildings, circus buildings, cafes, aqua parks, studios, mobile objects of medical purposes, hangars, garages, construction sites, service sta- tions and etc. Advantages of such objects are the possibility and simplicity of multiple instal- lation and demolition works. Their large-scale implementation is determined by temperature- moisture conditions under the shells.Analytical and calculating researches, real researches of thermodynamic parameters of heat and mass exchange, multifactorial processes of air in pneumobasic objects, their shells in a wide range of climatic parameters of air (January – December in the Republic of Belarus, in many geographical latitudes of many countries have shown that the limit of the possibility of optimizing wind loads, heat flow, acoustic effects is infinite (sports, residential, industrial, warehouse, the military-technical units (tanks, airplanes, etc.. In modeling of convective flows in pneumobasic objects (part 1 there are processes with higher dynamic parameters of the air flow for the characteristic pneumobasic object, carried out the calculation of the velocity field, temperature, pressure at the speed of access of air through the inflow holes up to 5 m/sec at the moments of times (20, 100, 200, 400 sec. The calculation was performed using the developed mathematical

The main objectives of this thesis are the direct numerical simulation of natural convection in a vertical differentially heated slot and the improvements of second-order turbulence modelling. A three-dimensional direct numerical simulation code has been developed in order to gain a better understanding of turbulence properties in natural convection flows. This code has been validated in several physical configurations: non-stratified natural convection flows (conduction solution), stratified natural convection flows (double boundary layer solution), transitional and turbulent Poiseuille flows. For the conduction solution, the turbulent regime was reached at a Rayleigh number of 1*10{sup 5} and 5.4*10{sup 5}. A detailed analysis of these results has revealed the principal qualities of the available models but has also pointed our their shortcomings. This data base has been used in order to improve the triple correlations transport models and to select the turbulent time scales suitable for such flows. (author). 122 refs., figs., tabs., 4 appends.

The present study is focused on Lapwood convection in isotropic porous media saturated with non-Newtonian shear thinning fluid. The non-Newtonian rheological behavior of the fluid is modeled using the general viscosity model of Carreau-Yasuda. The convection configuration consists of a shallow porous cavity with a finite aspect ratio and subject to a vertical constant heat flux, whereas the vertical walls are maintained impermeable and adiabatic. An approximate analytical solution is developed on the basis of the parallel flow assumption, and numerical solutions are obtained by solving the full governing equations. The Darcy model with the Boussinesq approximation and energy transport equations are solved numerically using a finite difference method. The results are obtained in terms of the Nusselt number and the flow fields as functions of the governing parameters. A good agreement is obtained between the analytical approximation and the numerical solution of the full governing equations. The effects of the rheological parameters of the Carreau-Yasuda fluid and Rayleigh number on the onset of subcritical convection thresholds are demonstrated. Regardless of the aspect ratio of the enclosure and thermal boundary condition type, the subcritical convective flows are seen to occur below the onset of stationary convection. Correlations are proposed to estimate the subcritical Rayleigh number for the onset of finite amplitude convection as a function of the fluid rheological parameters. Linear stability of the convective motion, predicted by the parallel flow approximation, is studied, and the onset of Hopf bifurcation, from steady convective flow to oscillatory behavior, is found to depend strongly on the rheological parameters. In general, Hopf bifurcation is triggered earlier as the fluid becomes more and more shear-thinning.

Large gradients in density and temperature occur near the edge in H-mode plasmas and in the core of tokamak plasmas with negative central shear. Transport in these regions may be comparable to neoclassical. Standard neoclassical theory does not apply when the gradient lengths are comparable to an ion orbit excursion, or banana width. A basic question for neoclassical transport in large gradient regions is: do ion-ion collisions drive particle transport? Near the plasma edge in H-mode, where ion orbit loss requires that the ion energy transport be convective, neoclassical particle transport due to ion-ion collisions may play an important role. In negative central shear plasmas, where transport is inferred to be near neoclassical, it is important to have accurate predictions for the neoclassical rate of energy and particle transport. A simple 2-D slab model has been used, with a momentum-conserving collision operator, to show that ion-ion collisions do drive particle transport. When the gradients are large, the open-quotes field particleclose quotes contribution to the particle flux is non-local, and does not cancel the open-quotes test particleclose quotes contribution, which is local. Solutions of the kinetic equation are found which show that the steepness of the density profile, for increasing particle flux, is limited by orbit averaging. The gradient length is limited by the thermal gyroradius, and the convective energy flux is independent of ion temperature. This will allow an ion thermal runaway to occur, if there are no other ion energy loss mechanisms

Optimization of natural convection-driven flows may provide significant improvements to the performance of cooling devices, but a theoretical investigation of such flows has been rarely done. The present paper illustrates an efficient gradient-based optimization method for analyzing such systems. We consider numerically the natural convection-driven flow in a differentially heated cavity with three Prandtl numbers (Pr=0.15{-}7) at super-critical conditions. All results and implementations were done with the spectral element code Nek5000. The flow is analyzed using linear direct and adjoint computations about a nonlinear base flow, extracting in particular optimal initial conditions using power iteration and the solution of the full adjoint direct eigenproblem. The cost function for both temperature and velocity is based on the kinetic energy and the concept of entransy, which yields a quadratic functional. Results are presented as a function of Prandtl number, time horizons and weights between kinetic energy and entransy. In particular, it is shown that the maximum transient growth is achieved at time horizons on the order of 5 time units for all cases, whereas for larger time horizons the adjoint mode is recovered as optimal initial condition. For smaller time horizons, the influence of the weights leads either to a concentric temperature distribution or to an initial condition pattern that opposes the mean shear and grows according to the Orr mechanism. For specific cases, it could also been shown that the computation of optimal initial conditions leads to a degenerate problem, with a potential loss of symmetry. In these situations, it turns out that any initial condition lying in a specific span of the eigenfunctions will yield exactly the same transient amplification. As a consequence, the power iteration converges very slowly and fails to extract all possible optimal initial conditions. According to the authors' knowledge, this behavior is illustrated here for

In this Letter, the problem of forced convection over a horizontal flat plate is presented and the homotopy perturbation method (HPM) is employed to compute an approximation to the solution of the system of nonlinear differential equations governing on the problem. It has been attempted to show the capabilities and wide-range applications of the homotopy perturbation method in comparison with the previous ones in solving heat transfer problems. The obtained solutions, in comparison with the exact solutions admit a remarkable accuracy. A clear conclusion can be drawn from the numerical results that the HPM provides highly accurate numerical solutions for nonlinear differential equations

The average convective heat transfer coefficient for a seated human body exposed to downward flow from above was determined. Thermal manikin with complex body shape and size of an average Scandinavian female was used. The surface temperature distribution of the manikin’s body was as the skin...... of the convective heat transfer coefficient of the whole body (hc [W/(m2•K)]) was proposed: hc=4.088+6.592V1.715 for a seated naked body at 20ºC and hc=2.874+7.427V1.345 for a seated naked body at 26ºC. Differences in the convective heat transfer coefficient of the whole body in low air velocity range, V

Full Text Available Osmotic dehydration is a process in which partial water is removed by immersion of water containing cellular solid in a concentrated aqueous solution of high osmotic media for a specific time and temperature. Preliminary trials were planned for finalizing the concentration of osmolyte (salt solution: 5%, 10%, 15% and 20%. The osmotically pre-treated samples were dried at 50 °C which were examined using sensory parameters. On the basis of sensory parameters, 15% salt solution concentration was considered best. The osmotically pre-treated jackfruit samples of 15% salt solution were convectively dehydrated in a tray dryer at air temperatures of 50, 60 and 70 °C at constant velocity of 1.5 m/s air flow in perforated trays. Results indicated that drying took place in falling rate period. The sample dried at 60 °C was found better in color as compared to samples at 50 and 70 °C. Mathematical models were fitted to the experimental data and the performance of these models was evaluated by comparing the coefficient of determination (R2, Root mean square error (RMSE, reduced chi-square (χ2, percent mean relative deviation modulus (E% between observed and predicted moisture ratio. The best model was chosen as one with the highest coefficient of correlation (R2; and the least χ2, RMSE and mean relative deviation modulus (E. Wang and Singh model, having χ2 and RMSE value (at 60 °C of 0.00027 and 0.01655 respectively gave the best results for describing the drying behavior of jackfruit samples.

We develop a Petrov-Galerkin stabilization method for multiscale convection-diffusion transport systems. Existing stabilization techniques add a limited number of degrees of freedom in the form of bubble functions or a modified diffusion, which may not be sufficient to stabilize multiscale systems. We seek a local reduced-order model for this kind of multiscale transport problems and thus, develop a systematic approach for finding reduced-order approximations of the solution. We start from a Petrov-Galerkin framework using optimal weighting functions. We introduce an auxiliary variable to a mixed formulation of the problem. The auxiliary variable stands for the optimal weighting function. The problem reduces to finding a test space (a dimensionally reduced space for this auxiliary variable), which guarantees that the error in the primal variable (representing the solution) is close to the projection error of the full solution on the dimensionally reduced space that approximates the solution. To find the test space, we reformulate some recent mixed Generalized Multiscale Finite Element Methods. We introduce snapshots and local spectral problems that appropriately define local weight and trial spaces. In particular, we use energy minimizing snapshots and local spectral decompositions in the natural norm associated with the auxiliary variable. The resulting spectral decomposition adaptively identifies and builds the optimal multiscale space to stabilize the system. We discuss the stability and its relation to the approximation property of the test space. We design online basis functions, which accelerate convergence in the test space, and consequently, improve stability. We present several numerical examples and show that one needs a few test functions to achieve an error similar to the projection error in the primal variable irrespective of the Peclet number.

Full Text Available Natural convection heat transfer and fluid flow have been examined numerically using the control-volume finite-element method in an isosceles prismatic cavity, submitted to a uniform heat flux from below when inclined sides are maintained isothermal and vertical walls are assumed to be perfect thermal insulators, without symmetry assumptions for the flow structure. The aim of the study is to examine a pitchfork bifurcation occurrence. Governing parameters on heat transfer and flow fields are the Rayleigh number and the aspect ratio of the enclosure. It has been found that the heated wall is not isothermal and the flow structure is sensitive to the aspect ratio. It is also found that heat transfer increases with increasing of Rayleigh number and decreases with increasing aspect ratio. The effects of aspect ratio become significant especially for higher values of Rayleigh number. Eventually the obtained results show that a pitchfork bifurcation occurs at a critical Rayleigh number, above which the symmetric solutions becomes unstable and asymmetric solutions are instead obtained.

Convection-resolving models (CRMs) can explicitly simulate deep convection and resolve interactions between convective updrafts. They are thus increasingly used in numerous weather and climate applications. However, the truncation of the continuous energy cascade at scales of O (1 km) poses a serious challenge, as in kilometer-scale simulations the size and properties of the simulated convective cells are often determined by the horizontal grid spacing (Δ x ).In this study, idealized simulations of deep moist convection over land are performed to assess the convergence behavior of a CRM at Δ x = 8, 4, 2, 1 km and 500 m. Two types of convergence estimates are investigated: bulk convergence addressing domain-averaged and integrated variables related to the water and energy budgets, and structural convergence addressing the statistics and scales of individual clouds and updrafts. Results show that bulk convergence generally begins at Δ x =4 km, while structural convergence is not yet fully achieved at the kilometer scale, despite some evidence that the resolution sensitivity of updraft velocities and convective mass fluxes decreases at finer resolution. In particular, at finer grid spacings the maximum updraft velocity generally increases, and the size of the smallest clouds is mostly determined by Δ x . A number of different experiments are conducted, and it is found that the presence of orography and environmental vertical wind shear yields more energetic structures at scales much larger than Δ x , sometimes reducing the resolution sensitivity. Overall the results lend support to the use of kilometer-scale resolutions in CRMs, despite the inability of these models to fully resolve the associated cloud field.

In this Letter, we report the influences of thermal time-lag on the onset of convection, its bifurcations and chaos of a horizontal layer of Boussinesq fluid heated underneath taking non-Fourier Cattaneo-Christov hyperbolic model for heat propagation. A five-dimensional nonlinear system is obtained for a low-order Galerkin expansion, and it reduces to Lorenz system for Cattaneo number tending to zero. The linear stability agreed with existing results that depend on Cattaneo number C. It also gives a threshold Cattaneo number, CT, above which only oscillatory solutions can persist. The oscillatory solutions branch terminates at the subcritical steady branch with a heteroclinic loop connecting a pair of saddle points for subcritical steady-state solutions. For subcritical onset of convection two stable solutions coexist, that is, hysteresis phenomenon occurs at this stage. The steady solution undergoes a Hopf bifurcation and is of subcritical type for small value of C, while it becomes supercritical for moderate Cattaneo number. The system goes through period-doubling/noisy period-doubling transition to chaos depending on the control parameters. There after the system exhibits Shil'nikov chaos via homoclinic explosion. The complexity of spiral strange attractor is analyzed using fractal dimension and return map.

Planetary magnetic fields are thought to be the product of hydromagnetic dynamo action. For Earth, this process occurs within the convecting, turbulent and rapidly rotating outer core, where the dynamics are characterized by low Rossby, low magnetic Prandtl and high Rayleigh numbers. Progress in studying dynamos has been limited by current computing capabilities and the difficulties in replicating the extreme values that define this setting. Asymptotic models that embrace these extreme parameter values and enforce the dominant balance of geostrophy provide an option for the study of convective flows with actual relevance to geophysics. The quasi-geostrophic dynamo model (QGDM) is a multiscale, fully-nonlinear Cartesian dynamo model that is valid in the asymptotic limit of low Rossby number. We investigate the QGDM using a simplified class of solutions that consist of a single horizontal wavenumber which enforces a horizontal structure on the solutions. This single mode study is used to explore multiscale time stepping techniques and analyze the influence of the magnetic field on convection.

The self-consistent theory of time-dependent convection in the earth's magnetotail of Schindler and Birn (1982) is extended to three dimensions to include more realistic tail geometry and three-dimensional flow. We confirm that a steady state solution implies unrealistic tail geometry or large particle or energy losses that are unrealistic during quiet times and conclude therefore that as in the 2-dimensional case the magnetotail becomes time-dependent for typical convection electric fields. Explicit solutions are derived, even analytically, for the three-dimensional flow and the electric and magnetic field in a realistic tail geometry, and quantitative examples are presented. Consequences of time-dependent convection are demonstrated considering two idealized cases of magnetosphere response to solar wind changes: (1) uniform compression as the likely consequence of increasing (static, dynamic or magnetic) solar wind pressure; and (2) compression only in the z direction perpendicular to the plasma sheet as the probable consequence of a dawn to dusk external electric field (E/sub y/>0), corresponding to a southward interplanetary magnetic field component (B/sub z/ 0 with geomagnetic activity. Several other features, already present in the 2-dimensional theory, are confirmed

The convection mixing model is proposed for low-energy high-current electron beam treatment of titanium alloys, pre-processed by heterogeneous plasma flows generated via explosion of carbon tape and powder TiB2. The model is based on the assumption vortices in the molten layer are formed due to the treatment by concentrated energy flows. These vortices evolve as the result of thermocapillary convection, arising because of the temperature gradient. The calculation of temperature gradient and penetration depth required solution of the heat problem with taking into account the surface evaporation. However, instead of the direct heat source the boundary conditions in phase transitions were changed in the thermal conductivity equation, assuming the evaporated material takes part in the heat exchange. The data on the penetration depth and temperature distribution are used for the thermocapillary model. The thermocapillary model embraces Navier-Stocks and convection heat transfer equations, as well as the boundary conditions with the outflow of evaporated material included. The solution of these equations by finite elements methods pointed at formation of a multi-vortices structure when electron-beam treatment and its expansion over new zones of material. As the result, strengthening particles are found at the depth exceeding manifold their penetration depth in terms of the diffusion mechanism.

Oxidation reactions of thiourea by chlorite in a Hele-Shaw cell are excitable, autocatalytic, exothermic, and generate a lateral instability upon being triggered by the autocatalyst. Reagent concentrations used to develop convective instabilities delivered a temperature jump at the wave front of 2.1 K. The reaction zone was 2 mm and due to normal cooling after the wave front, this generated a spike rather than the standard well-studied front propagation. The reaction front has solutal and thermal contributions to density changes that act in opposite directions due to the existence of a positive isothermal density change in the reaction. The competition between these effects generates thermal plumes. The fascinating feature of this system is the coexistence of plumes and fingering in the same solution which alternate in frequency as the front propagates, generating hot and cold spots within the Hele-Shaw cell, and subsequently spatiotemporal inhomogeneities. The small ΔT at the wave front generated thermocapillary convection which competed effectively with thermogravitational forces at low Eötvös Numbers. A simplified reaction-diffusion-convection model was derived for the system. Plume formation is heavily dependent on boundary effects from the cell dimensions. This work was supported by Grant No. CHE-1056366 from the NSF and a Research Professor Grant from the University of KwaZulu-Natal.

This research thesis addresses the field of fluid-wall thermal exchanges in which the notion of exchange coefficient is notably useful to design, size and optimise devices. A first part reports a bibliographical study which gives an overview of solutions envisaged to determine the convection coefficient in permanent regime with the use of flow sensors, as well as in transient regime. Then, the author reports the development of an unsteady method which is based on the analysis of the cooling kinetics of the front face of a convecting wall, after a unique energetic perturbation (an infinitely brief pulse, or a finite duration energy step). This method is applied to the general case (wall with finite thickness) and to the case of a semi-infinite wall which is typical of materials which are weak thermal conductors. This is extended to the case of good thermal conductors by considering a thermally thin wall. After a detailed description of the experimental bench, above-mentioned solutions are applied to insulating and good thermal conducting materials. In order to validate results of an analysis in transient regime, they are compared with measurements performed in permanent regime with a flow-metering technique. The study of the principle of the dissipation-based flow sensor, and its operation are reported. Experimental results are presented for both methods (pulse and flow sensor), and compared in order to highlight the interest of the unsteady method [French] Difficile a mesurer, le coefficient de convection reste cependant une grandeur necessaire au calcul et a l'optimisation de tout systeme thermique. L'amelioration des capteurs thermiques permet aujourd'hui de concevoir une methode optique, utilisable a distance, et non destructive. Nous proposons dans ce but, un procede de mesure en regime transitoire base sur la radiometrie photothermique impulsionnelle. L'analyse du regime de relaxation d'une paroi, apres une brusque elevation de temperature, permet de remonter

A complete synoptic-scale vorticity budget was related to convection storm development in the eastern two-thirds of the United States. The 3-h sounding interval permitted a study of time changes of the vorticity budget in areas of convective storms. Results of analyses revealed significant changes in values of terms in the vorticity equation at different stages of squall line development. Average budgets for all areas of convection indicate systematic imbalance in the terms in the vorticity equation. This imbalance resulted primarily from sub-grid scale processes. Potential instability in the lower troposphere was analyzed in relation to the development of convective activity. Instability was related to areas of convection; however, instability alone was inadequate for forecast purposes. Combinations of stability and terms in the vorticity equation in the form of indices succeeded in depicting areas of convection better than any one item separately.

Convective circulations and vortices are common features of atmospheres that absorb low-entropy-energy at higher temperatures than they reject high-entropy-energy to space. These circulations range from small to planetary-scale and play an important role in the vertical transport of heat, momentum, and tracer species. Thus, the development of theoretical models for convective phenomena is important to our understanding of many basic features of planetary atmospheres. A thermodynamically general theory for convective circulations and vortices is proposed. The theory includes irreversible processes and quantifies the pressure drop between the environment and any point in a convective updraft. The article's main result is that the proposed theory provides an expression for the pressure drop along streamlines or streamtubes that is a generalization of Bernoulli's equation to convective circulations. We speculate that the proposed theory not only explains the intensity, but also shed light on other basic features of convective circulations and vortices.

Recent studies on thermo-electro-hydrodynamic (TEHD) convection are reviewed with focus on investigations motivated by the analogy with natural convection. TEHD convection originates in the action of the dielectrophoretic force generated by an alternating electric voltage applied to a dielectric fluid with a temperature gradient. This electrohydrodynamic force is analogous to Archimedean thermal buoyancy and can be regarded as a thermal buoyancy force in electric effective gravity. The review is concerned with TEHD convection in plane, cylindrical, and spherical capacitors under microgravity conditions, where the electric gravity can induce convection without any complexities arising from geometry or the buoyancy force due to the Earth’s gravity. We will highlight the convection in spherical geometry, comparing developed theories and numerical simulations with the GEOFLOW experiments performed on board the International Space Station (ISS). (paper)

This communication addresses the magnetohydrodynamic (MHD) three dimensional flow of Sisko nanofluid bounded by a surface stretched bidirectionally. Nanofluid model includes the Brownian motion and thermophoresis. Heat transfer through convective condition is discussed. Developed condition with the zero nanoparticles mass flux at the surface is implemented. The governing problems subject to boundary layer approximations are computed for the convergent series solutions. Effects of interesting flow parameters on the temperature and nanoparticles concentration distributions are studied and discussed. Skin friction coefficients and the local Nusselt number are computed and analyzed. - Highlights: • Three-dimensional flow of Sisko nanofluid is modeled. • Uniform applied magnetic field is adopted. • Brownian motion and thermophoresis effects are accounted. • Heat transfer convective condition is utilized. • Recently constructed condition with zero nanoparticles mass flux is implemented.

Magnetohydrodynamic (MHD) doubly stratified flow of Maxwell nanofluid in presence of mixed convection is analyzed in this article. Effects of thermophoresis, Brownian motion and heat generation/absorption are present. The flow is induced due to linear stretching of sheet. Mathematical formulation is made under boundary layer approach. Expressions of velocity, temperature and nanoparticles concentration are developed. The obtained results are plotted and discussed to examine the variations in temperature and nanoparticles concentration due to different physical parameters. Numerical computations are made to obtain the values of local Nusselt and Sherwood numbers. Impact of sundry parameters on the flow quantities is analyzed graphically. - Highlights: • Double stratified flow of Maxwell nanofluid with mixed convection is modeled. • Thermophoresis and Brownian motion effects are encountered. • Computations are made to obtain the solution expressions. • Numerical values of local Nusselt and Sherwood numbers are computed and examined.

Full Text Available This paper presents a numerical study of natural convective flow of an electrically conducting viscous micropolar fluid past a vertical plate. Internal heat generation (IHG versus without IHG in the medium are discussed in the context of corresponding similarity solutions. Results are presented in terms of velocity, angular velocity, temperature, skin friction in tabular forms, local wall-coupled stress, and Nusselt number. Computations have been accomplished by parametrizing the micropolar, micro-rotation, magnetic field, suction parameters, and the Prandtl number. Several critical issues are addressed at the end of the paper with reference to a previous study by El-Hakiem. The study is relevant to high-temperature electromagnetic materials fabrication systems. Keywords: Natural convection, Thermal boundary layer, Micropolar fluid, Similarity transformation, Internal heat generation

Full Text Available Present work is devoted to convective flow of ferrofluid due to non linear stretching curved sheet. Electrically conducting fluid is considered in the presence of uniform magnetic field. Nanofluid comprises water and magnetite-Fe3O4 as nanoparticles. Thermal radiation and heat generation/absorption are explained. Homotopy concept is utilized for the development of solutions. Highly nonlinear partial differential systems are reduced into the nonlinear ordinary differential system. Impact of non-dimensional radius of curvature and power law index on the physical quantities like fluid pressure, velocity and temperature field are examined. Computations for surface shear stress and heat transfer rate also analyzed. Keywords: MHD nanofluid, Thermal radiation, Porous medium, Convective boundary conditions, Non-linear curved stretching sheet

Full Text Available This paper models the peristaltic transport of magnetohydrodynamic (MHD third grade nanofluid in a curved channel with wall properties. Combined effects of heat and mass transfer are retained via mixed convection. The present analysis is made in the presence of thermal radiation and chemical reaction. No-slip effect is maintained at the boundary for the velocity, temperature and nanoparticle volume fraction. Resulting formulation is simplified by employing the assumptions of long wavelength and low Reynolds number approximations. Results of axial velocity, temperature, nanoparticle mass transfer and heat transfer are studied graphically. Results reveal increment in fluid velocity for larger values of heat transfer Grashof number. There is reduction in nanoparticle mass transfer with the increase in thermophoresis parameter. Keywords: Peristalsis, Third grade nanofluid, Curved channel, Mixed convection, Thermal radiation, Chemical reaction, Flexible walls, Numerical solutions

Transient forced convective boiling is of practical importance in relation to the accident analysis of nuclear reactor etc. For large length-to-diameter ratio, the transient boiling characteristics are predicted by transient two-phase flow calculations. Based on homogeneous model of two-phase flow, the transient forced convective boiling for power and flow transients are analysed. Analytical expressions of various parameters of transient two-phase flow have been obtained for several simple cases of power and flow transients. Based on these results, heat flux, velocity and time at transient CHF condition are predicted analytically for step and exponential power increases, and step, exponential and linear velocity decreases. The effects of various parameters on heat flux, velocity and time at transient CHF condition have been clarified. Numerical approach combined with analytical method is proposed for more complicated cases. Solution method for pressure transient are also described. (author)

Forced convection transient heat transfer for helium gas at various periods of exponential increase of heat input to a horizontal cylinder and a plate (ribbon) one was experimentally and theoretically studied. In the experimental studies, the authors measured heat flux, surface temperature, and transient heat transfer coefficients for forced convection flow of helium gas over a horizontal cylinder and a plate (ribbon) one under wide experimental conditions. Empirical correlations for quasi-steady-state heat transfer and transient heat transfer were obtained based on the experimental data. In the theoretical study, transient heat transfer was numerically solved based on a turbulent flow model. The values of numerical solution for surface temperature and heat flux were compared and discussed with authors' experimental data. (author)

The computer code analyzing the system operating and transient behavior must distinguish flow conditions involved with convective heat transfer flow regimes. And the proper correlations must be supplied to those flow regimes. However the existing safety analysis codes are focused on the Light Water Reactor and they are skeptical to be applied to the GCRs (Gas Cooled Reactors). One of the technical issues raise by the development of the VHTR is the mixed convection, which occur when the driving forces of both forced and natural convection are of comparable magnitudes. It can be encountered as in channel of the stacked with fuel elements and a decay heat removal system and in VHTR. The mixed convection is not intermediate phenomena with natural convection and forced convection but independent complicated phenomena. Therefore, many researchers have been studied and some primary issues were propounded for phenomena mixed convection. This paper is to discuss some problems identified through reviewing the papers for mixed convection phenomena. And primary issues of mixed convection heat transfer were proposed respect to thermal hydraulic problems for VHTR. The VHTR thermal hydraulic study requires an indepth study of the mixed convection phenomena. In this study we reviewed the classical flow regime map of Metais and Eckert and derived further issues to be considered. The following issues were raised: (1) Buoyancy aided an opposed flows were not differentiated and plotted in a map. (2) Experimental results for UWT and UHF condition were also plotted in the same map without differentiation. (3) The buoyancy coefficient was not generalized for correlating with buoyancy coefficient. (4) The phenomenon analysis for laminarization and returbulization as buoyancy effects in turbulent mixed convection was not established. (5) The defining to transition in mixed convection regime was difficult.

One of the key factors controlling convective cloud systems in the Madden-Julian Oscillation (MJO) over the tropical Indian Ocean is the property of the atmospheric boundary layer. Convective downdrafts and precipitation from the cloud systems produce cold pools in the boundary layer, which can inhibit subsequent development of convection. The recovery time is the time it takes for the boundary layer to return to pre convective conditions. It may affect the variability of the convection on various time scales during the initiation of MJO. This study examines the convective cold pool structure and boundary layer recovery using the NOAA WP-3D aircraft observations, include the flight-level, Doppler radar, and GPS dropsonde data, collected during the Dynamics of MJO (DYNAMO) field campaign from November-December 2011. The depth and strength of convective cold pools are defined by the negative buoyancy, which can be computed from the dropsonde data. Convective downdraft can be affected by environmental water vapor due to entrainment. Mid-level dry air observed during the convectively suppressed phase of MJO seems to enhance convective downdraft, making the cold pools stronger and deeper. Recovery of the cold pools in the boundary layer is determined by the strength and depth of the cold pools and also the air-sea heat and moisture fluxes. Given that the water vapor and surface winds are distinct for the convectively active and suppressed phases of MJO over the Indian Ocean, the aircraft data are stratified by the two different large-scale regimes of MJO. Preliminary results show that the strength and depth of the cold pools are inversely correlated with the surrounding mid-level moisture. During the convectively suppressed phase, the recovery time is ~5-20 hours in relative weak wind condition with small air-sea fluxes. The recovery time is generally less than 6 hours during the active phase of MJO with moist mid-levels and stronger surface wind and air-sea fluxes.

The study aims to determine suitable position and strategy in order to reach superiority in convection business based on the company strengths and weaknesses. A study conducted in late 2012 at AR Vendor, a home-based convection company which focus on the t-shirt screen printing service. In response to the issue of the below average profit margin, the company has to rethink their position and strategy in handling the convection business environment. While AR Vendor business may growth in accor...

Achieving distribution of gene-carrying vectors is a major barrier to the clinical application of gene therapy. Because of the blood-brain barrier, the distribution of genetic vectors to the central nervous system (CNS) is even more challenging than delivery to other tissues. Direct intraparenchymal microinfusion, a minimally invasive technique, uses bulk flow (convection) to distribute suspensions of macromolecules widely through the extracellular space (convection-enhanced delivery [CED]). Although acute injection into solid tissue is often used for delivery of oligonucleotides, viruses, and liposomes, and there is preliminary evidence that certain of these large particles can spread through the interstitial space of the brain by the use of convection, the use of CED for distribution of viruses in the brain has not been systematically examined. That is the goal of this study. Investigators used a rodent model to examine the influence of size, osmolarity of buffering solutions, and surface coating on the volumetric distribution of virus-sized nanoparticles and viruses (adeno-associated viruses and adenoviruses) in the gray matter of the brain. The results demonstrate that channels in the extracellular space of gray matter in the brain are large enough to accommodate virus-sized particles and that the surface characteristics are critical determinants for distribution of viruses in the brain by convection. These results indicate that convective distribution can be used to distribute therapeutic viral vectors in the CNS.

In dry, shear-free convective boundary layers (CBLs), the turbulent flow of air is known to organise itself on large scales into coherent, cellular patterns, or superstructures, consisting of fast, narrow updraughts and slow, wide downdraughts which together form circulations. Superstructures act as transport mechanisms from the surface to the top of the boundary layer and vice-versa, as opposed to small-scale turbulence, which only modifies conditions locally. This suggests that a thorough investigation into superstructure properties may help us better understand transport across the atmospheric boundary layer as a whole. Whilst their existence has been noted, detailed studies into superstructures in the CBL have been scarce. By applying methods which are known to successfully isolate similar large-scale patterns in turbulent Rayleigh-Bénard convection, we can assess the efficacy of those detection techniques in the CBL. In addition, through non-dimensional analysis, we can systematically compare superstructures in various convective regimes. We use direct numerical simulation of four different cases for intercomparison: Rayleigh-Bénard convection (steady), Rayleigh-Bénard convection with an adiabatic top lid (quasi-steady), a stably-stratified CBL (quasi-steady) and a neutrally-stratified CBL (unsteady). The first two are non-penetrative and the latter two penetrative. We find that although superstructures clearly emerge from the time-mean flow in the non-penetrative cases, they become obscured by temporal averaging in the CBL. This is because a rigid lid acts to direct the flow into counter-rotating circulation cells whose axis of rotation remains stationary, whereas a boundary layer that grows in time and is able to entrain fluid from above causes the circulations to not only grow in vertical extent, but also to move horizontally and merge with neighbouring circulations. Spatial filtering is a useful comparative technique as it can be performed on boundary

A new method for the solution of nonlinear dispersive partial differential equations is described. The marker method relies on the definition of a convective field associated with the underlying partial differential equation; the information about the approximate solution is associated with the response of an ensemble of markers to this convective field. Some key aspects of the method, such as the selection of the shape function and the initial loading, are discussed in some details

It is commonly assumed that buoyancy in the fluid core powers the geodynamo. We study here the minimal model of a convection driven dynamo, which is a horizontal plane layer in a gravity field, filled with electrically conducting fluid, heated from below and cooled from above, and rotating about a vertical axis. Such a plane layer may be viewed as a local approximation to the geophysically more relevant spherical geometry. The numerical simulations have been run on graphics processing units with at least 960 cores. If the convection is driven stronger and stronger at fixed rotation rate, the flow behaves at some point as if it was not rotating. This transition shows in the scaling of the heat transport which can be used to distinguish slow from rapid rotation. One expects dynamos to behave differently in these two flow regimes. But even within the convection flows which are rapidly rotating according to this criterion, it will be shown that different types of dynamos exist. In one state, the magnetic field strength obeys a scaling indicative of a magnetostrophic balance, in which the Lorentz force is in equilibrium with the Coriolis force. The flow in this case is helical. A different state exists at higher magnetic Reynolds numbers, in which the magnetic energy obeys a different scaling law and the helicity of the flow is much reduced. As one increases the Rayleigh number, all other parameters kept constant, one may find both types of dynamos separated by an interval of Rayleigh numbers in which there are no dynamos at all. The effect of these transitions on energy dissipation and mean field generation have also been studied.

Over tropical oceans, widely scattered convection of various depths may or may not grow upscale into mesoscale convective systems (MCSs). But what distinguishes the large-scale environment that favors such upscale growth from that favoring "unorganized", scattered convection? Is it some combination of large-scale low-level convergence and ascending motion, combined with sufficient instability? We recently put this to a test with ERA-I reanalysis data, with disappointing results. The "usual suspects" of total column water vapor, large-scale ascent, and CAPE may all be required to some extent, but their differences between large MCSs and scattered convection are small. The main positive results from this work (already published) demonstrate that the strength of convection is well correlated with the size and perhaps "organization" of convective features over tropical oceans, in contrast to tropical land, where strong convection is common for large or small convective features. So, important questions remain: Over tropical oceans, how should we define "organized" convection? By size of the precipitation area? And what environmental conditions lead to larger and better organized MCSs? Some recent attempts to answer these questions will be described, but good answers may require more data, and more insights.

Natural Convection in Composite Fluid-Porous Domains provides a timely overview of the current state of understanding on the phenomenon of convection in composite fluid-porous layers. Natural convection in horizontal fluid-porous layers has received renewed attention because of engineering problems such as post-accident cooling of nuclear reactors, contaminant transport in groundwater, and convection in fibrous insulation systems. Because applications of the problem span many scientific domains, the book serves as a valuable resource for a wide audience.

The research presented in this dissertation addresses a fundamental question regarding urban, ultimately anthropogenic, influences on convection as it relates to lightning production and precipitation structure...

The structure of multiscale convection in a thermally stratified plane horizontal fluid layer is investigated by means of numerical simulations. The thermal diffusivity is assumed to produce a thin boundary sublayer convectively much more unstable than the bulk of the layer. The simulated flow is a superposition of cellular structures with three different characteristic scales. In contrast to the largest convection cells, the smaller ones are localised in the upper portion of the layer. The smallest cells are advected by the larger-scale convective flows. The simulated flow pattern qualitatively resembles that observed on the Sun.

Cumulus convection plays a significant role in determining the structure of the terrestrial water vapor field. Cumulus convection acts directly on the moisture field by condensing and precipitating water vapor and by redistributing water vapor through cumulus induced eddy circulations. The mechanisms by which cumulus convection influences the terrestrial water vapor distribution is outlined. Calculations using a theory due to Kuo is used to illustrate the mechanisms by which cumulus convection works. Understanding of these processes greatly aids the ability of researchers to interpret the seasonal and spatial distribution of atmospheric water vapor by providing information on the nature of sources and sinks and the global circulation.

Past laboratory experiments of thermo chemical convection have dealt with systems involving fluids with different intrinsic densities and viscosities in a Rayleigh-Bénard setup. Although these experiments have greatly improved our understanding of the Earth's mantle dynamics, they neglect a fundamental component of planetary convection: internal heat sources. We have developed a microwave-based method in order to study convection and mixing in systems involving two layers of fluid with different densities, viscosities, and internal heat production rates. Our innovative laboratory experiments are appropriate for the early Earth, when the lowermost mantle was likely enriched in incompatible and heat producing elements and when the heat flux from the core probably accounted for a small fraction of the mantle heat budget. They are also relevant to the present-day mantle if one considers that radioactive decay and secular cooling contribute both to internal heating. Our goal is to quantify how two fluid layers mix, which is still very difficult to resolve accurately in 3-D numerical calculations. Viscosities and microwave absorptions are tuned to achieve high values of the Rayleigh-Roberts and Prandtl numbers relevant for planetary convection. We start from a stably stratified system where the lower layer has higher internal heat production and density than the upper layer. Due to mixing, the amount of enriched material gradually decreases to zero over a finite time called the lifetime. Based on more than 30 experiments, we have derived a scaling law that relates the lifetime of an enriched reservoir to the layer thickness ratio, a, to the density and viscosity contrasts between the two layers, and to their two different internal heating rates in the form of an enrichment factor beta=1+2*a*H1/H, where H1 is the heating rate of the lower fluid and H is the average heating rate. We find that the lifetime of the lower enriched reservoir varies as beta**(-7/3) in the low

After an overview of researches on natural convection in a confined or semi-confined environment, this research thesis reports the use of the Caltagirone and Mojtabi numerical model and the study of its validity for different values of the Rayleigh and Prandtl numbers. Results obtained with this model are compared with experimental ones. Thermal transfer curves are presented and discussed, as well as the different temperature fields numerically obtained, flow function fields, velocities in the fluid layer, and temperature profiles with respect to the Rayleigh number [fr

The principle of speckle photography can be applied to the measurement of density variations in fluids. A modification of existing experimental arrangements allows for the measurement of large values of the light deflection angles as they may occur in heat and mass transfer situations. The method is demonstrated for the case of a helium jet exhausting into still air and the natural convective flow along a heated plate. The obtained data are compared with results measured with classical optical interferometers, and good agreement is found. The advantages of the new technique over the classical optical methods are briefly discussed. 11 references

The nonlinear statistical growth rate eq for convective cells driven by drift-wave (DW) interactions is studied with the aid of a covariant Hamiltonian formalism for the gyrofluid nonlinearities. A statistical energy theorem is proven that relates eq to a second functional tensor derivative of the DW energy. This generalizes to a wide class of systems of coupled partial differential equations a previous result for scalar dynamics. Applications to (i) electrostatic ion-temperature-gradient-driven modes at small ion temperature, and (ii) weakly electromagnetic collisional DW's are noted

The effect of negative aerodynamic drag in an ideal fluid subject to convective instability is considered. It is shown that a cylinder moving in such a fluid is propelled forward in its motion by the convective forces and that the characteristic acceleration time is comparable to the onset time of convective motions in the fluid. It is suggested that convective propulsion plays an important role in the dynamics of flux tubes extending through the surface of the sun. The suppression of the upward heat flow in a Boussinesq convective cell with free upper and lower boundaries by a downdraft is then analyzed. Application to the solar convection zone indicates that downdrafts of 1 to 2 km/s at depths of 1000 to 4000 km beneath the visible surface of the sun are sufficient to reduce the upward heat flux to a small fraction of the ambient value.

This second part of a two-part study uses Weather Research and Forecasting simulations with aquachannel and aquapatch domains to investigate the time evolution of convectively coupled Kelvin waves (CCKWs). Power spectra, filtering, and compositing are combined with object-tracking methods to assess the structure and phase speed propagation of CCKWs during their strengthening, mature, and decaying phases. In this regard, we introduce an innovative approach to more closely investigate the wave (Kelvin) versus entity (super cloud cluster or "SCC") dualism. In general, the composite CCKW structures represent a dynamical response to the organized convective activity. However, pressure and thermodynamic fields in the boundary layer behave differently. Further analysis of the time evolution of pressure and low-level moist static energy finds that these fields propagate eastward as a "moist" Kelvin wave (MKW), faster than the envelope of organized convection or SCC. When the separation is sufficiently large the SCC dissipates, and a new SCC generates to the east, in the region of strongest negative pressure perturbations. We revisit the concept itself of the "coupling" between convection and dynamics, and we also propose a conceptual model for CCKWs, with a clear distinction between the SCC and the MKW components.

Using direct numerical simulations of vertical natural convection (VNC) at Rayleigh numbers 1 . 0 ×105 - 1 . 0 ×109 and Prandtl number 0 . 709 , we provide support for a generalised applicability of the Grossmann-Lohse (GL) theory, originally developed for horizontal natural (Rayleigh-Bénard) convection. In accordance with the theory, the boundary-layer thicknesses of the velocity and temperature fields in VNC obey laminar-like scaling, whereas away from the walls, the dissipation of the turbulent fluctuations obey the scaling for fully developed turbulence. In contrast to Rayleigh-Bénard convection, the direction of gravity in VNC is parallel to the mean flow. Thus, there no longer exists an exact relation linking the normalised global dissipations to the Nusselt, Rayleigh and Prandtl numbers. Nevertheless, we show that the unclosed term, namely the global-averaged buoyancy flux, also exhibits laminar and turbulent scaling, consistent with the GL theory. The findings suggest that, similar to Rayleigh-Bénard convection, a pure power-law relationship between the Nusselt, Rayleigh and Prandtl numbers is not the best description for VNC and existing empirical power-law relationships should be recalibrated to better reflect the underlying physics.

Double-diffusive convection (DDC), which is the buoyancy-driven flow with fluid density depending on two scalar components, is ubiquitous in many natural and engineering environments. Of great interests are scalars’ transfer rate and flow structures. Here we systematically investigate DDC flow

Tropical convection associated with convectively coupled Kelvin waves (CCKWs) is typically organized by an eastward-moving synoptic-scale convective envelope with numerous embedded westward-moving mesoscale disturbances. It is of central importance to assess upscale impact of mesoscale disturbances on CCKWs as mesoscale disturbances propagate at various tilt angles and speeds. Here a simple multi-scale model is used to capture this multi-scale structure, where mesoscale fluctuations are directly driven by mesoscale heating and synoptic-scale circulation is forced by mean heating and eddy transfer of momentum and temperature. The two-dimensional version of the multi-scale model drives the synoptic-scale circulation, successfully reproduces key features of flow fields with a front-to-rear tilt and compares well with results from a cloud resolving model. In the scenario with an elevated upright mean heating, the tilted vertical structure of synoptic-scale circulation is still induced by the upscale impact of mesoscale disturbances. In a faster propagation scenario, the upscale impact becomes less important, while the synoptic-scale circulation response to mean heating dominates. In the unrealistic scenario with upward/westward tilted mesoscale heating, positive potential temperature anomalies are induced in the leading edge, which will suppress shallow convection in a moist environment. In its three-dimensional version, results show that upscale impact of mesoscale disturbances that propagate at tilt angles (110o 250o) induces negative lower-tropospheric potential temperature anomalies in the leading edge, providing favorable conditions for shallow convection in a moist environment, while the remaining tilt angle cases have opposite effects. Even in the presence of upright mean heating, the front-to-rear tilted synoptic-scale circulation can still be induced by eddy terms at tilt angles (120o 240o). In the case with fast propagating mesoscale heating, positive

The C/O ratio produced during core helium burning affects the future evolution and nucleosynthetic yield of massive stars. This ratio is shown to be sensitive to the treatment of convection as well as uncertainties in nuclear rates. By minimizing the effect of semi-convection and reducing the size of the convective core, mass loss in OB stars increases the C/O ratio. (Author)

Novel high-resolution convection-permitting regional climate simulations over the US employing the pseudo-global warming approach are used to investigate changes in the convective population and thermodynamic environments in a future climate. Two continuous 13-year simulations were conducted using (1) ERA-Interim reanalysis and (2) ERA-Interim reanalysis plus a climate perturbation for the RCP8.5 scenario. The simulations adequately reproduce the observed precipitation diurnal cycle, indicating that they capture organized and propagating convection that most climate models cannot adequately represent. This study shows that weak to moderate convection will decrease and strong convection will increase in frequency in a future climate. Analysis of the thermodynamic environments supporting convection shows that both convective available potential energy (CAPE) and convective inhibition (CIN) increase downstream of the Rockies in a future climate. Previous studies suggest that CAPE will increase in a warming climate, however a corresponding increase in CIN acts as a balancing force to shift the convective population by suppressing weak to moderate convection and provides an environment where CAPE can build to extreme levels that may result in more frequent severe convection. An idealized investigation of fundamental changes in the thermodynamic environment was conducted by shifting a standard atmospheric profile by ± 5 °C. When temperature is increased, both CAPE and CIN increase in magnitude, while the opposite is true for decreased temperatures. Thus, even in the absence of synoptic and mesoscale variations, a warmer climate will provide more CAPE and CIN that will shift the convective population, likely impacting water and energy budgets on Earth.

A better representation of the diurnal cycle of convective precipitation is essential for the analysis of the energy balance and the water budget components such as runoff, evaporation and infiltration. Convection-permitting regional climate modeling (CPM) has been shown to improve the models' performance of summer precipitation, allowing to: (1) simulate the mesoscale processes in more detail and (2) to provide more insights in future changes in convective precipitation under climate change. In this work we investigate the skill of the Weather Research and Forecast model (WRF) in simulating the summer precipitation diurnal cycle over most of North America. We use 4 km horizontal grid spacing in a 13-years long current and future period. The future scenario is assuming no significant changes in large-scale weather patterns and aims to answer how the weather of the current climate would change if it would reoccur at the end of the century under a high-end emission scenario (Pseudo Global Warming). We emphasize on a region centered on the lee side of the Canadian Rocky Mountains, where the summer precipitation amount shows a regional maximum. The historical simulations are capable to correctly represent the diurnal cycle. At the lee-side of the Canadian Rockies the increase in the convective available potential energy as well as pronounced low-level moisture flux from the southeast Prairies explains the local maximum in summer precipitation. The PGW scenario shows an increase in summer precipitation amount and intensity in this region, consistently with a stronger source of moisture and convective energy.

Three deep convective cloud cases were selected during the 2011 Mid-Latitude Continental Convective Clouds Experiment (MC3E). Although biomass burning smoke advected from Mexico and Central America was the dominant source of cloud condensation nuclei (CCN) for deep convective cloud formation, the 11 May, 20 May, and 23 May cases exhibited different convective characteristics. The convection in the 11 May and 23 May cases formed in smoke laden environments in the presence of convective available potential energy (CAPE) values exceeding 1000 m2 s-2 and 3000 m2 s-2 along with low-level (0-1 km) shear of 10.3 m s-1 and 5.1 m s-1, respectively. The 11 May case had linear convection while the 23 May case featured discrete supercells. The 20 May case featured elevated linear convection that formed in a more moist environment with cleaner aerosol conditions, weak CAPE (9 km) suggesting a warm rain suppression mechanism caused by a combination of strong aerosol loading, large CAPE, and weak low-level wind shear. The observed results for the 20 May and 23 May cases agree well with recent modeling studies that simulated the convection and precipitation in these cases. Furthermore, the modeling of the 11 May case is suggested since the abundant amount of smoke CCN did not greatly enhance the overall precipitation amount and could be a possible aerosol-induced precipitation suppression case.

The linear stability properties of fluid convection in a vertical slot were studied. We use a Fourier-Chebychev decomposition was used to set up the linear eigenvalue problems for the Vertical Slot Convection and Benard problems. The eigenvalues, neutral stability curves, and critical point values of the Grashof number, G, and the wavenumber were determined. Plots of the real and imaginary parts of the eigenvalues as functions of G and α are given for a wide range of the Prandtl number, Pr, and special note is made of the complex mode that becomes linearly unstable above Pr ∼ 12.5. A discussion comparing different special cases facilitates the physical understanding of the VSC equations, especially the interaction of the shear-flow and buoyancy induced physics. Making use of the real and imaginary eigenvalues and the phase properties of the eigenmodes, the eigenmodes were characterized. One finds that the mode structure becomes progressively simpler with increasing Pr, with the greatest complexity in the mid ranges where the terms in the heat equation are of roughly the same size

Mesoscale convective systems (MCSs) are important contributors to the hydrologic cycle in many regions of the world as well as major sources of severe weather. MCSs continue to challenge forecasters and researchers alike, arising from difficulties in understanding system initiation, propagation, and demise. One distinct type of MCS is that formed from individual convective cells initiated primarily by daytime heating over high terrain. This work is aimed at improving our understanding of the land surface sensitivity of this class of MCS in the contiguous United States. First, a climatology of mesoscale convective systems originating in the Rocky Mountains and adjacent high plains from Wyoming southward to New Mexico is developed through a combination of objective and subjective methods. This class of MCS is most important, in terms of total warm season precipitation, in the 500 to 1300m elevations of the Great Plains (GP) to the east in eastern Colorado to central Nebraska and northwest Kansas. Examining MCSs by longevity, short lasting MCSs (15 hrs) reveals that longer lasting systems tend to form further south and have a longer track with a more southerly track. The environment into which the MCS is moving showed differences across commonly used variables in convection forecasting, with some variables showing more favorable conditions throughout (convective inhibition, 0-6 km shear and 250 hPa wind speed) ahead of longer lasting MCSs. Other variables, such as convective available potential energy, showed improving conditions through time for longer lasting MCSs. Some variables showed no difference across longevity of MCS (precipitable water and large-scale vertical motion). From subsets of this MCS climatology, three regions of origin were chosen based on the presence of ridgelines extending eastward from the Rocky Mountains known to be foci for convection initiation and subsequent MCS formation: Southern Wyoming (Cheyenne Ridge), Colorado (Palmer divide) and

Recent studies of propagating waves in an oscillatory convection of binary mixtures arise questions about transport properties of this flow. Optical visualization of a field of refraction index due to a shadowgraph technique gives information on the temperature and concentration fields. However, experimental observation of rolls propagating along the cell as travelling waves (TW) does not necessarily imply that mass is transferred hydrodynamically by the convective motion along the cell. One of the possibilities discussed, e.g., is that TW observed is only a phase propagation. The traditional examples of such situations come from the domain of linear, superposition-oriented physics. Acoustic waves transfer momentum and energy, but do not cause the mass to make excursions for their equilibrium point that are larger than the oscillation amplitude. In the case of nonlinear physics we were aware that small amplitude surface waves cause only small oscillatory motion round the equilibrium point, while larger amplitudes can cause the mass to start moving in the direction of the TW. This paper discussed the different possibilities of mass transfer by TW. 27 refs., 20 figs

In a sodium layer heated from below and cooled from above, the integral Nusselt numbers are determined in a range of Rayleigh numbers 1.5x10 3 5 . The experiments are performed in containers with dimensions of 500 mm in diameter and 15 mm and 45 mm in height. The relevant quantities are evaluated from measured temperature and heating power data. The experiments show that the heat transfer across the layer is determined mainly by heat conduction up to Rayleigh number Ra ≅ 10 4 . Beyond this value a significant increase of the convective heat transport is observed. At a Rayleigh number of 4x10 4 the Nusselt number achieves the value Nu = 1.7. This result differs from values given by Nusselt-Rayleigh number correlations reported in the literature for liquids with higher Prandtl number. A regression analysis of the experimental data results empirical correlations for the Nusselt number. A time series analysis of the time dependent temperature signals shows that the measured temperature fluctuations exhibit predominantly stochastic features. However, in the lower range of Rayleigh numbers 1.5x10 3 4 certain regular frequencies can be identified from peaks in broadband power density spectra. These frequencies correspond to fluctuations of a period of 80 to 200 seconds. These regular frequencies are explained by instabilities of the cellular pattern in the convection layer reported in the literature. (orig./HP) [de

In the present study, the non-Boussinesq effect in the thermal convection in an air-filled horizontal concentric annulus is studied numerically by using the variable property-based lattice Boltzmann flux solver (VPLBFS), with the radial temperature difference ratio of 1.0, the radius ratio of 2.0, and the Rayleigh number in the range 104 ≤ Ra ≤ 106. Several solutions are obtained by using the standard form or simplified versions of the VPLBFS, including the real solution with the total variation in fluid properties considered, named as the variable property solution (VPS), the constant property solution (CPS) based on the Boussinesq approximation, the solution with variable dynamic viscosity (VVS), the solution based on the partial Boussinesq approximation (PBAS), the solution with variable thermal conductivity (VCS) and the solution with variable fluid density (VDS). The discrepancy between these solutions is analyzed to illuminate the influence of the non-Boussinesq effects induced by partial or total variation in fluid properties on flow instability behaviors and heat transfer characteristics. The present study reveals the complicated flow instability behavior under non-Boussinesq conditions and its tight association with heat transfer characteristics. Also, it demonstrates the necessity of considering the integral effect of the total variation in fluid properties and highlights the essential role of the fluid density variation.

Simplified formulas for the heat fluxes with given parameters of the air are used to calculate the specific heat losses by convection in a number of solar-energy systems (water heater, thermal generator, double-glazed window, and still). Heat losses by convection and radiation are compared.

Thermal homogenization is essentially a transient problem and convective heat transfer by (chaotic) advection is known to accelerate this process. Convective heat transfer traditionally is examined in terms of heat-transfer coefficients at domain walls and characterised by Nusselt relations.

), and travelling convection vortices (TCVs). Furthermore, the large-scale ionospheric convection configuration has also demonstrated a strong correspondence to variations in the interplanetary medium and substorm activity. This report briefly discusses the progress made over the past decade in studies...

Modulated Rayleigh-Benard convection is analyzed for high frequencies and large modulation amplitudes. The linear theory of Gershuni and Zhukhovitskii is generalized to the nonlinear domain, and a subcritical bifurcation to convection is found in agreement with the experiments of Niemela and Donnelly. The crossover between the high-frequency (''Stokes layer'') regime and the low-frequency regime studied previously is analyzed

Time-resolved irradiance and convective heating and cooling of fast-response thermopile sensors were measured in 13 natural and prescribed wildland fires under a variety of fuel and ambient conditions. It was shown that a sensor exposed to the fire environment was subject to rapid fluctuations of convective transfer whereas irradiance measured by a windowed sensor was...

Natural convection and vapor loss from underground waste storage tanks is examined here. Stability criteria are provided for the onset of natural convection flow within the headspace of a tank, and between tanks and the environment. The flowrate is quantified and used to predict vapor losses during storage

In this paper natural convection in RPR reactor is analysed. The effect of natural convection valves size on cladding temperature is studied. The reactor channel heat transfer problem is solved using finite elements in a two-dimensional analysis. Results show that two valves with Φ = 0.16 m are suited to keep coolant and cladding temperatures below 73 0 C. (author) [pt

Two-dimensional numerical simulations are used to examine the interaction of acoustic waves with a compressible convecting fluid. Acoustic waves are forced at the lower boundary of the computational domain and propagate through a three-layer system undergoing vigorous penetrative convection. Energy exchange between the wave and the fluid is analyzed using a work integral formulation

Analog experiments have played an important role in the constructing ideas of mantle dynamics. The series of experiments by H. Ramberg is one of the successful examples. Recently, however the realm of the analog experiments seems to be overwhelmed by steady progress of computer simulations. Is there still room for the analog experiments? This might be a main and hidden subject of this session. Here we propose a working hypothesis how the convecting mantle behaves based on the analog experiments in the system of viscous fluid and particles. The essential part is the interaction of convecting flow with heterogeneities existing in the boundaries. It is proposed the preexisting topographical heterogeneity in the boundary could control the flow pattern of convecting fluid. If this kind of heterogeneity can be formed as a consequence of convective motion and mobilized by the flow, the convection also can control the heterogeneity. We can expect interactions in two ways, by which the system behaves in a self-organize fashion. To explore the mutual interactions between convection flow and heterogeneity the system of viscous fluid and particles with slightly higher density is selected as 2D Rayleigh-Benard type convection. The basic structure consists of a basal particulate layer where permeable convection transports heat and an upper viscous fluid layer. By reducing the magnitude of the density difference the convective flow can mobilize the particles and can erode the basal layer. The condition of this erosion can be identified in the phase diagram of the particle Shields"f and the Rayleigh numbers. At Ra greater than 107 the convection style drastically changed before and after the erosion. Before the erosion where the flat interface of the boundary is maintained small scaled turbulent convection pattern is dominant. After the erosion where the interface becomes bumpy the large scale convective motion is observed. The structure is coherent to that of the boundary. This

A solute-blocking model is presented that provides a kinetic explanation of osmosis and ideal solution thermodynamics. It validates a diffusive model of osmosis that is distinct from the traditional convective flow model of osmosis. Osmotic equilibrium occurs when the fraction of water molecules in solution matches the fraction of pure water molecules that have enough energy to overcome the pressure difference. Solute-blocking also provides a kinetic explanation for why Raoult's law and the other colligative properties depend on the mole fraction (but not the size) of the solute particles, resulting in a novel kinetic explanation for the entropy of mixing and chemical potential of ideal solutions. Some of its novel predictions have been confirmed; others can be tested experimentally or by simulation.

A solute-blocking model is presented that provides a kinetic explanation of osmosis and ideal solution thermodynamics. It validates a diffusive model of osmosis that is distinct from the traditional convective flow model of osmosis. Osmotic equilibrium occurs when the fraction of water molecules in solution matches the fraction of pure water molecules that have enough energy to overcome the pressure difference. Solute-blocking also provides a kinetic explanation for why Raoult’s law and the other colligative properties depend on the mole fraction (but not the size) of the solute particles, resulting in a novel kinetic explanation for the entropy of mixing and chemical potential of ideal solutions. Some of its novel predictions have been confirmed, others can be tested experimentally or by simulation. PMID:27225298

Internal pressurization and convective gas flow, which can aerate wetland plants more efficiently than diffusion, are common in temperate species. Here, we present the first survey of convective flow in a range of tropical plants. The occurrence of pressurization and convective flow was determined...... in 20 common wetland plants from the Mekong Delta in Vietnam. The diel variation in pressurization in culms and the convective flow and gas composition from stubbles were examined for Eleocharis dulcis, Phragmites vallatoria and Hymenachne acutigluma, and related to light, humidity and air temperature....... Nine of the 20 species studied were able to build up a static pressure of >50Pa, and eight species had convective flow rates higher than 1mlmin-1. There was a clear diel variation, with higher pressures and flows during the day than during the night, when pressures and flows were close to zero...

The buoyancy driven convective flow fields are steady circulatory flows which were made between surfaces maintained at two fixed temperatures. They are ubiquitous in nature and play an important role in many engineering applications. Especially, in last decades, natural convection in a close loop or cavity becomes the main issue in the molecular biology for the polymerase chain reaction (PCR). Application of a natural convection can reduce the costs and efforts remarkably. This paper focuses on the sensitivity study of turbulence analysis using CFD for a natural convection in a closed rectangular cavity. Using commercial CFD code, FLUENT, various turbulent models were applied to the turbulent flow. Results from each CFD model will be compared each other in the viewpoints of flow characteristics. This work will suggest the best turbulent model of CFD for analyzing turbulent flows of the natural convection in an enclosure system

Full Text Available The mathematical generalization of classical model of the global circuit with taking into account the convective current generator, working in the planetary boundary layer was considered. Convective current generator may be interpreted as generator, in which the electromotive force is generated by processes, of the turbulent transport of electrical charge. It is shown that the average potential of ionosphere is defined not only by the thunderstorm current generators, working at the present moment, but by the convective current generator also. The influence of the convective processes in the boundary layer on the electrical parameters of the atmosphere is not only local, but has global character as well. The numerical estimations, made for the case of the convective-unstable boundary layer demonstrate that the increase of the average potential of ionosphere may be of the order of 10% to 40%.

Injection of a neutral beam into a plasma in a magnetic field has been studied by means of numerical plasma simulations. It is found that, in the absence of a rotational transform, the convection electric field arising from the polarization charges at the edges of the beam is dissipated by turbulent plasma convection, leading to anomalous plasma diffusion across the magnetic field. The convection electric field increases with the beam density and beam energy. In the presence of a rotational transform, polarization charges can be neutralized by the electron motion along the magnetic field. Even in the presence of a rotational transform, a steady-state convection electric field and, hence, anomalous plasma diffusion can develop when a neutral beam is constantly injected into a plasma. Theoretical investigations on the convection electric field are described for a plasma in the presence of rotational transform. 11 refs., 19 figs

Concentration gradients in a fluid adjacent to a reactive surface due to contrast in surface reactivity generate convective flows. These flows result from contributions by electro- and diffusio-osmotic phenomena. In this study, we have analyzed reactive patterns that release and consume protons, analogous to bimetallic catalytic conversion of peroxide. Similar systems have typically been studied using either scaling analysis to predict trends or costly numerical simulation. Here, we present a simple analytical model, bridging the gap in quantitative understanding between scaling relations and simulations, to predict the induced potentials and consequent velocities in such systems without the use of any fitting parameters. Our model is tested against direct numerical solutions to the coupled Poisson, Nernst-Planck, and Stokes equations. Predicted slip velocities from the model and simulations agree to within a factor of ≈2 over a multiple order-of-magnitude change in the input parameters. Our analysis can be used to predict enhancement of mass transport and the resulting impact on overall catalytic conversion, and is also applicable to predicting the speed of catalytic nanomotors.

Full Text Available A whole single cherry tomato was dried in a forced convective micro-dryer. The experiments were carried out at constant air velocity and humidity and temperatures of 50, 60, 70 °C. In order to study the effect of the skin, two sets of experiments were performed using a tomato with and without skin (easily removed. Shorter drying times were obtained when increasing drying temperatures as well as when removing sample skin. X-ray microtomography, a non-destructive 3D imaging technique was used to follow shrinkage of the samples. This phenomenon was introduced in the modelling part of this study. Analytical solutions of the Fick’law were used to determine the diffusion coefficient at the three temperatures studied, and then the activation energy was obtained through fitting the Arrhenius equation. The skin effect was clearly evidenced by showing that the mass transfer parameter values of an original tomato with skin were largely smaller than the one without skin. Indeed, the moisture effective diffusivity ranged from 2.56×10-11 to 7.67×10-11 m2·s-1 with activation energy of 50430 J·mol-1 for tomato with skin an ranged from 4.59×10-10 m2·s-1 to 6.73×10-10 m2·s-1 with activation energy of 17640 J.mol-1 for tomato without skin.

A clay-powder, cement, and water-base plugging solution is proposed having reduced solution viscosity characteristics while maintaining tensile strength in cement stone. This solution utilizes silver graphite and its ingredients, by mass weight, are as follows: cement 51.2-54.3%; claypowder 6.06-9.1%; silver graphite 0.24-0.33%; with water making up the remainder.

Highlights: • The paper presents experimental and analytical results of Pb–Li eutectic alloy forced convection flow. • Analytical results are in good agreement with ones of hydrogen permeation in Pb–Li forced convection flow. • The results are useful for the design of liquid blanket of fusion reactors. - Abstract: Transient- or steady-state hydrogen permeation from a primary fluid of Li{sub 17}Pb{sub 83} (Pb–Li) through a permeable tube of Inconel-625 alloy to a secondary Ar purge is investigated experimentally under a forced convection flow in a dual cylindrical tube system. Results of the overall hydrogen permeation flux are correlated in terms of diffusivity, solubility and an average axial velocity of Pb–Li and diffusivity and solubility of the solid wall. Analytical solutions under proper assumptions are derived to simulate the transient- and steady-state rates of the overall hydrogen permeation, and close agreement is obtained between experiment and analysis. Two things are clarified from the comparison: (i) how the steady-state permeation rate is affected by the mass-transfer properties and the average velocity of Pb–Li and the properties of Inconel-625, and (ii) how its transient behavior is done by the diffusivity of the two materials. The results obtained here will give important information to estimate or to analyze the tritium transfer rate in fluidized Pb–Li blankets of DEMO or the future commercial fusion reactors.

The work presents results of numerical simulations of natural convection in cavity formed by the surfaces of two horizontal coaxial cylinders. The temperature of the outer cylinder is constant. The area between the cylinders is filled with an ideal incompressible fluid. The inner cylinder is set as the heater. The solution of the equations of thermal convection in a two-dimensional approximation performed by the software package ANSYS Fluent with finite volume method. The study compares the results of numerical simulation with several well-known theoretical and experimental results. The nature of interaction of the inner cylinder with a convection current created in the gap was observed. It was shown that the flux appeared around a heated cylinder affects the weight of the heat source and causes an additional lift force from the surrounding fluid. The various Rayleigh numbers (from 1.0 ṡ 103 to 1.5 ṡ 106) and fluid with different Prandtl number (from 0.5 to 1.0 ṡ 105) are considered.

Theoretical and computational studies of the modulational interaction between trapped ion convective cells and short wavelength drift wave turbulence are discussed. These studies are motivated by the fact that cells and drift waves are expected to coexist in tokamaks so that: (a) cells strain and modulate drift waves, and (b) drift waves open-quote ride on close-quote a background of cells. The results of the authors' investigation indicate that: (1) (nonlinear) parametric growth rates of trapped ion convective cells can exceed linear predictions (for drift wave levels at the mixing length limit); (2) a set of coupled envelope equations, akin to the Zakharov equations from Langmuir turbulence, can be derived and used to predict the formation of a dipole pair of convective cells trapped by the drift wave envelope. This dipole pair is strongly anisotropic, due to the structure of the drift wave Reynolds stress which drives the cell flow. Numerical solutions of the envelope equations are in good agreement with theoretical predictions, and indicate the persistence of the structure in time; (3) strong modulation and trapping of drift waves with k perpendicular ρ > 1 occurs. Extensions to magnetically sheared systems and the broader implications of this work as a paradigm for the dynamics of persistent structures in shearing flows are discussed

One of the cooling modes for any source of heat such as in a shutdown nuclear core is the natural convection. The design specifications of any cooling pool can only be done when the removal heat rate and the corresponding mass flow rate is reasonably established. In our simulation scheme, we assumed that the body forces acting in the cubic water cell are: the weight, the drag force and the integrated pressure forces on the horizontal surfaces, the viscosity shear forces on the vertical surfaces and also a special viscosity drag force due to the mass dislocation along a Bernoulli type current tube outside the motive region. For a suitable time step, the uprising convection velocity is determined by an implicit and also by an explicit solution algorithm. The resulting differential equation depends on updating specific mass, dynamic viscosity and constant pressure heat coefficient with the last known temperature in the cell that absorbed heat. Numerical calculation software was performed using MATLAB’s technical computing language and then applied for a heat generation plate simulating a spent fuel assembler from a shutdown nuclear core. The results show time evolution of convection, terminal velocity and water temperature distribution. Pool dimension as well as pool level decrement are also determined for various air exhausting system conditions and heat rate of the spent fuel plate being cooled. (author)

One of the cooling modes for any source of heat such as in a shutdown nuclear core is the natural convection. The design specifications of any cooling pool can only be done when the removal heat rate and the corresponding mass flow rate is reasonably established. In our simulation scheme, we assumed that the body forces acting in the cubic water cell are: the weight, the drag force and the integrated pressure forces on the horizontal surfaces, the viscosity shear forces on the vertical surfaces and also a special viscosity drag force due to the mass dislocation along a Bernoulli type current tube outside the motive region. For a suitable time step, the uprising convection velocity is determined by an implicit and also by an explicit solution algorithm. The resulting differential equation depends on updating specific mass, dynamic viscosity and constant pressure heat coefficient with the last known temperature in the cell that absorbed heat. Numerical calculation software was performed using MATLAB’s technical computing language and then applied for a heat generation plate simulating a spent fuel assembler from a shutdown nuclear core. The results show time evolution of convection, terminal velocity and water temperature distribution. Pool dimension as well as pool level decrement are also determined for various air exhausting system conditions and heat rate of the spent fuel plate being cooled. (author)

Full Text Available Radiation and heat generation effects in unsteady magnetohydrodynamic mixed convection flow of nanofluids along a vertical channel are investigated. Silver nanoparticles of spherical shapes and of different sizes in water as a convection-al base fluid are incorporated. The purpose of this study is to measure the effect of different sizes of nanoparticles on velocity and temperature. Keeping in mind the size, particle material, shape, clustering and Brownian motion of nanoparticles, Koo and Kleinstreuer model is used. The problem is modeled in terms of partial differential equations with physical boundary conditions. Analytical solutions are obtained for velocity and temperature, plotted and discussed. It is concluded that increasing the size of Ag nanoparticles (up to specific size, 30 nm, results in a very small velocity increment while for large particle size (30-100 nm, no change in velocity is observed. As the small size of nanoparticles has the highest thermal conductivity and viscosity. This change in velocity with size of nano-particles is found only in water-based nanofluids with low volume fraction 0.01 while at low volume concentration, no change is observed.

Improved lumped parameter models were developed for the transient heat conduction in multi-layer composite slabs subjected to combined convective and radiative cooling. The improved lumped models were obtained through two-point Hermite approximations for integrals. Transient combined convective and radiative cooling of three-layer composite slabs was analyzed to illustrate the applicability of the proposed lumped models, with respect to different values of the Biot numbers, the radiation-conduction parameter, the dimensionless thermal contact resistances, the dimensionless thickness, and the dimensionless thermal conductivity. It was shown by comparison with numerical solution of the original distributed parameter model that the higher order lumped model (H 1,1 /H 0,0 approximation) yielded significant improvement of average temperature prediction over the classical lumped model. In addition, the higher order (H 1,1 /H 0,0 ) model was applied to analyze the transient heat conduction problem of steel-concrete-steel sandwich plates. - Highlights: → Improved lumped models for convective-radiative cooling of multi-layer slabs were developed. → Two-point Hermite approximations for integrals were employed. → Significant improvement over classical lumped model was achieved. → The model can be applied to high Biot number and high radiation-conduction parameter. → Transient heat conduction in steel-concrete-steel sandwich pipes was analyzed as an example.

Full Text Available Polymerase chain reaction (PCR has been one of the principal techniques of molecular biology and diagnosis for decades. Conventional PCR platforms, which work by rapidly heating and cooling the whole vessel, need complicated hardware designs, and cause energy waste and high cost. On the other hand, partial heating on the various locations of vessels to induce convectivesolution flows by buoyancy have been used for DNA amplification in recent years. In this research, we develop a new convective PCR platform, capillary loop convective polymerase chain reaction (clcPCR, which can generate one direction flow and make the PCR reaction more stable. The U-shaped loop capillaries with 1.6 mm inner diameter are designed as PCR reagent containers. The clcPCR platform utilizes one isothermal heater for heating the bottom of the loop capillary and a CCD device for detecting real-time amplifying fluorescence signals. The stable flow was generated in the U-shaped container and the amplification process could be finished in 25 min. Our experiments with different initial concentrations of DNA templates demonstrate that clcPCR can be applied for precise quantification. Multiple sample testing and real-time quantification will be achieved in future studies.

Full Text Available Climate models project an increase in heavy precipitation events in response to greenhouse gas forcing. Important elements of such events are rain showers and thunderstorms, which are poorly represented in models with parameterized convection. In this study, simulations with 12 km horizontal grid spacing (convection-parameterizing model, CPM and 2 km grid spacing (convection-resolving model, CRM are employed to investigate the change in the diurnal cycle of convection with warmer climate. For this purpose, simulations of 11 days in June 2007 with a pronounced diurnal cycle of convection are compared with surrogate simulations from the same period. The surrogate climate simulations mimic a future climate with increased temperatures but unchanged relative humidity and similar synoptic-scale circulation. Two temperature scenarios are compared: one with homogeneous warming (HW using a vertically uniform warming and the other with vertically dependent warming (VW that enables changes in lapse rate.The two sets of simulations with parameterized and explicit convection exhibit substantial differences, some of which are well known from the literature. These include differences in the timing and amplitude of the diurnal cycle of convection, and the frequency of precipitation with low intensities. The response to climate change is much less studied. We can show that stratification changes have a strong influence on the changes in convection. Precipitation is strongly increasing for HW but decreasing for the VW simulations. For cloud type frequencies, virtually no changes are found for HW, but a substantial reduction in high clouds is found for VW. Further, we can show that the climate change signal strongly depends upon the horizontal resolution. In particular, significant differences between CPM and CRM are found in terms of the radiative feedbacks, with CRM exhibiting a stronger negative feedback in the top-of-the-atmosphere energy budget.

Climate models project an increase in heavy precipitation events in response to greenhouse gas forcing. Important elements of such events are rain showers and thunderstorms, which are poorly represented in models with parameterized convection. In this study, simulations with 12 km horizontal grid spacing (convection-parameterizing model, CPM) and 2 km grid spacing (convection-resolving model, CRM) are employed to investigate the change in the diurnal cycle of convection with warmer climate. For this purpose, simulations of 11 days in June 2007 with a pronounced diurnal cycle of convection are compared with surrogate simulations from the same period. The surrogate climate simulations mimic a future climate with increased temperatures but unchanged relative humidity and similar synoptic-scale circulation. Two temperature scenarios are compared: one with homogeneous warming (HW) using a vertically uniform warming and the other with vertically dependent warming (VW) that enables changes in lapse rate. The two sets of simulations with parameterized and explicit convection exhibit substantial differences, some of which are well known from the literature. These include differences in the timing and amplitude of the diurnal cycle of convection, and the frequency of precipitation with low intensities. The response to climate change is much less studied. We can show that stratification changes have a strong influence on the changes in convection. Precipitation is strongly increasing for HW but decreasing for the VW simulations. For cloud type frequencies, virtually no changes are found for HW, but a substantial reduction in high clouds is found for VW. Further, we can show that the climate change signal strongly depends upon the horizontal resolution. In particular, significant differences between CPM and CRM are found in terms of the radiative feedbacks, with CRM exhibiting a stronger negative feedback in the top-of-the-atmosphere energy budget.

This study aimed at producing experimental results and developing a new heat transfer correlation based upon a semi-empirical buoyancy coefficient. Mixed convection mass transfers inside horizontal pipe were investigated for the pipe of various length-to-diameters with varying Re. Forced convection correlation was developed using a very short cathode. With the length of cathode increase and Re decrease, the heat transfer rates were enhanced and becomes higher than that of forced convection. An empirical buoyancy coefficient was derived from correlation of natural convection and forced convection with the addition of L/D. And the heat transfer correlation for laminar mixed convection was developed using the buoyancy coefficient, it describes not only current results, but also results of other studies. Mixed convection occurs when the driving forces of both forced and natural convections are of comparable magnitude (Gr/Re 2 ∼1). It is classical problem but is still an active area of research for various thermal applications such as flat plate solar collectors, nuclear reactors and heat exchangers. The effect of buoyancy on heat transfer in a forced flow is varied by the direction of the buoyancy force. In a horizontal pipe the direction of the forced and buoyancy forces are perpendicular. The studies on the mixed convections of the horizontal pipes were not investigated very much due to the lack of practical uses compared to those of vertical pipes. Even the definitions on the buoyancy coefficient that presents the relative influence of the forced and the natural convections, are different by scholars. And the proposed heat transfer correlations do not agree

Interfacial mass-transport and redistribution in the micro-scale liquid droplets are important in diverse fields of research interest. The role of the "inflow" and the "outflow" type convective eddy-pairs in the entrainment of outer solute and internal relocation are examined for different homogeneous and heterogeneous water droplet pairs appearing in a tandem arrangement. Two micro-droplets of pure (rain) water interact with an oncoming outer air stream (Re ≤ 100) contaminated by uniformly distributed SO2. By virtue of separation/attachment induced non-uniform interfacial shear-stress gradient, the well-defined inflow/outflow type pairs of recirculating eddy-based convective motion quickly develops, and the eddies effectively attract/repel the accumulated outer solute and control the physical process of mass-transport in the droplet-pair. The non-uniformly shear-driven flow interaction and bifurcation of the circulatory internal flow lead to growth of important micro-scale "secondary" eddies which suitably regroup with the adjacent "primary" one to create the sustained inflow/outflow type convective dynamics. The presently derived flow characteristics and in-depth analysis help to significantly improve our understanding of the micro-droplet based transport phenomena in a wider context. By tuning "Re" (defined in terms of the droplet diameter and the average oncoming velocity of the outer air) and gap-ratio "α," the internal convective forcing and the solute entrainment efficiency could be considerably enhanced. The quantitative estimates for mass entrainment, convective strength, and saturation characteristics for different coupled micro-droplet pairs are extensively examined here for 0.2 ≤ α ≤ 2.0 and 30 ≤ Re ≤ 100. Interestingly, for the compound droplets, with suitably tuned radius-ratio "B" (of upstream droplet with respect to downstream one) the generated "inflow" type coherent convective dynamics helped to significantly augment the centre

Extensive numerical studies of the dynamo equations due to the global convection are presented to simulate the solar cycle and to open the way to study general stellar magnetic cycles. The dynamo equations which represent the longitudinally-averaged magnetohydrodynamical action (mean magnetohydrodynamics) of the global convection under the influence of the rotation in the solar convection zone are considered here as an initial boundary-value problem. The latitudinal and radial structure of the dynamo action consisting of a generation action due to the differential rotation and a regeneration action due to the global convection is parameterized in accordance with the structure of the rotation and of the global convection. This is done especially in such a way as to represent the presence of the two cells of the regeneration action in the radial direction in which the action has opposite signs, which is typical of the regeneration action of the global convection. The effects of the dynamics of the global convection (e.g., the effects of the stratification of the physical conditions in the solar convection zone) are presumed to be all included in those parameters used in the model and they are presumed not to alter the results drastically since these effects are only to change the structure of the regeneration action topologically. (Auth.)

Observations suggest that both the high- and low-latitude boundary layers contribute to magnetospheric convection, and that their contributions are linked. In the interpretation pursued here, the high-latitude boundary layer (HBL) generates the voltage while the low-latitude boundary layer (LBL) generates the current for the part of the convection electric circuit that closes through the ionosphere. This paper gives a model that joins the high- and low-latitude boundary layers consistently with the ionospheric Ohm's law. It describes an electric circuit linking both boundary layers, the region 1 Birkeland currents, and the ionospheric Pedersen closure currents. The model works by using the convection electric field that the ionosphere receives from the HBL to determine two boundary conditions to the equations that govern viscous LBL-ionosphere coupling. The result provides the needed self-consistent coupling between the two boundary layers and fully specifies the solution for the viscous LBL-ionosphere coupling equations. The solution shows that in providing the current required by the ionospheric Ohm's law, the LBL needs only a tenth of the voltage that spans the HBL. The solution also gives the latitude profiles of the ionospheric electric field, parallel currents, and parallel potential. It predicts that the plasma in the inner part of the LBL moves sunward instead of antisunward and that, as the transpolar potential decreases below about 40 kV, reverse polarity (region 0) currents appear at the poleward border of the region 1 currents. A possible problem with the model is its prediction of a thin boundary layer (∼1000 km), whereas thicknesses inferred from satellite data tend to be greater

Compressible convection is ubiquitous in large natural systems such Planetary atmospheres, stellar and planetary interiors. Its modelling is notoriously more difficult than the case when the Boussinesq approximation applies. One reason for that difficulty has been put forward by Ogura and Phillips (1961): the compressible equations generate sound waves with very short time scales which need to be resolved. This is why they introduced an anelastic model, based on an expansion of the solution around an isentropic hydrostatic profile. How accurate is that anelastic model? What are the conditions for its validity? To answer these questions, we have developed a numerical model for the full set of compressible equations and compared its solutions with those of the corresponding anelastic model. We considered a simple rectangular 2D Rayleigh-Bénard configuration and decided to restrict the analysis to infinite Prandtl numbers. This choice is valid for convection in the mantles of rocky planets, but more importantly lead to a zero Mach number. So we got rid of the question of the interference of acoustic waves with convection. In that simplified context, we used the entropy balances (that of the full set of equations and that of the anelastic model) to investigate the differences between exact and anelastic solutions. We found that the validity of the anelastic model is dictated by two conditions: first, the superadiabatic temperature difference must be small compared with the adiabatic temperature difference (as expected) ɛ = Δ TSA / delta Ta << 1, and secondly that the product of ɛ with the Nusselt number must be small.

The flow of plasma in the Earth's magnetotail cannot reach a steady state, since adiabatic convection would lead to exceedingly high pressure of the associated magnetic flux tubes closer to the Earth, the so-called pressure catastrophe. The natural way to avoid the pressure catastrophe is to significantly reduce the flux tube volume by reconnection, and observations show a near-Earth reconnection line typically around 20-25 Earth radii down tail. Earthward flows from this reconnection line are rather bursty and typically seen outside of 10 Earth radii. At this point they are strongly braked by the here dominant dipolar magnetic field. The pressure gradients piled up by the flow lead to the substorm current wedge, and possibly other substorm phenomena observed in the Earth's ionosphere. When more and more flux tubes are piled up, the dipolarization front moves tailward and finally shuts off near-Earth reconnection

This book reviews the field of helioseismology and its outstanding challenges and also offers a detailed discussion of the latest computational methodologies. The focus is on the development and implementation of techniques to create 3-D images of convection and magnetism in the solar interior and to introduce the latest computational and theoretical methods to the interested reader. With the increasing availability of computational resources, demand for greater accuracy in the interpretation of helioseismic measurements and the advent of billion-dollar instruments taking high-quality observations, computational methods of helioseismology that enable probing the 3-D structure of the Sun have increasingly become central. This book will benefit students and researchers with proficiency in basic numerical methods, differential equations and linear algebra who are interested in helioseismology.

Understanding the long-term generation of planetary or stellar magnetic field requires complementary knowledge of the large-scale fluid dynamics pervading large fractions of the object's interior. Such large-scale motions are sensitive to the system's geometry which, in planets and stars, is spherical to a good approximation. As a result, computational models designed to study such systems often solve the MHD equations in spherical geometry, frequently employing a spectral approach involving spherical harmonics. We present computational and user-interface design aspects of one such modeling tool, the Rayleigh convection code, which is suitable for deployment on desktop and petascale-hpc architectures alike. In this poster, we will present an overview of this code's parallel design and its built-in diagnostics-output package. Rayleigh has been developed with NSF support through the Computational Infrastructure for Geodynamics and is expected to be released as open-source software in winter 2017/2018.

The occurrence of flow excursion instability during passive heat removal for Tehran Research Reactor (TRR) has been analyzed at low-pressure and low-mass rate of flow conditions without boiling taking place. Pressure drop-flow rate characteristics in the general case are determined upon a developed code for this purpose. The code takes into account variations of different pressure drop components caused by different powers as well as different core inlet temperatures. The analysis revealed the fact that the instability can actually occur in the natural convection mode for a range of powers per fuel plates at a predetermined inlet temperature with fixed geometry of the core. Low mass rate of flow and high sub-cooling are the two important conditions for the occurrence of static instability in the TRR. The calculated results are compared with the existing data in the literature. (author)

This Brief describes and analyzes flow and heat transport over a liquid-saturated porous bed. The porous bed is saturated by a liquid layer and heating takes place from a section of the bottom. The effect on flow patterns of heating from the bottom is shown by calculation, and when the heating is sufficiently strong, the flow is affected through the porous and upper liquid layers. Measurements of the heat transfer rate from the heated section confirm calculations. General heat transfer laws are developed for varying porous bed depths for applications to process industry needs, environmental sciences, and materials processing. Addressing a topic of considerable interest to the research community, the brief features an up-to-date literature review of mixed convection energy transport in fluid superposed porous layers.

Infrared (IR) thermography, because of its two-dimensional and non-intrusive nature, can be exploited in industrial applications as well as in research. This paper deals with measurement of convective heat transfer coefficients (h) in three complex fluid flow configurations that concern the main aspects of both internal and external cooling of turbine engine components: (1) flow in ribbed, or smooth, channels connected by a 180 degrees sharp turn, (2) a jet in cross-flow, and (3) a jet impinging on a wall. The aim of this study was to acquire detailed measurements of h distribution in complex flow configurations related to both internal and external cooling of turbine components. The heated thin foil technique, which involves the detection of surface temperature by means of an IR scanning radiometer, was exploited to measure h. Particle image velocimetry was also used in one of the configurations to precisely determine the velocity field.

Full Text Available Several recent papers have investigated the two-dimensional stagnation point flow of an upper-convected Maxwell fluid by employing a similarity change of variable to reduce the governing PDEs to a nonlinear third order ODE boundary value problem (BVP. In these previous works, the BVP was studied numerically and several conjectures regarding the existence and behavior of the solutions were made. The purpose of this article is to mathematically verify these conjectures. We prove the existence of a solution to the BVP for all relevant values of the elasticity parameter. We also prove that this solution has monotonically increasing first derivative, thus verifying the conjecture that no ``overshoot'' of the boundary condition occurs. Uniqueness results are presented for a large range of parameter space and bounds on the skin friction coefficient are calculated.

The similarity theory of Phillips (Deep Sea Res. 13, 1966) for the convectively induced motion in the Red Sea, predicts that the outflow buoyancy difference should scale as (B _0L) ^2/3/h :: , where B 0 is the surface buoyancy flux and L and h are the length and height of the channel above the sill crest, respectively. A friction-buoyancy balance leads to a modified expression [(B _0L) ^2/3/h][fracLh]^1/3 :: (2). The results can be applied also to a number of other natural flows including freezing-induced convection in fjords and polar seas. A series of Experiments have been conducted to check the predictions. A channel 300 cm long and 21 cm wide has been constructed. Within it segmented salt-water sources have been placed over a length of 250 cm. Their depth varied from 2 to 12 cm. A sill was placed in the exit region and its height was at least half the total depth of water in the channel. Density data were taken by withdrawing samples while velocity profiles were found by a DPIV technique. The meanflow consists of a two-layer stratification over a large fraction of the length of the channel. Our results suggest that the scaling (2) above is most closely realized with a constant of value 1.1. Analysis of the Red Sea data suggests a constant between 1.1 and 1.4 depending on the data set used. The exit Fr-number is unity. The amount of mixing within the channel is less than that predicted for the 'overmixed' state. Supported by the German Acad. Exchge. Serv. and the NSF Polar Programs.

Reverse convection towers have attracted attention as a medium for cleansing modern cities. Evaporation of an aqueous mist injected at the tower opening could generate electrical power by creating descent, and simultaneously scavenge unsightly and unhealthful particulates. The study offered here assesses the influence to tower water droplets on the photochemical component of Los Angeles type smog. The primary radical chain initiator OH is likely removed into aqueous phases well within the residence time of air in the tower, and then reacts away rapidly. Organics do not dissolve, but nighttime hydrolysis of N{sub 2}O{sub 5} depletes the nitrogen oxides. A lack of HOx would slow hydrocarbon oxidation and so also ozone production. Lowering of NOx would also alter ozone production rates, but the direction is uncertain. SO{sub 2} is available in sufficient quantities in some urban areas to react with stable oxidants, and if seawater were the source of the mist, the high pH would lead to fast sulfur oxidation kinetics. With an accommodation coefficient of 10{sup {minus}3}, however, ozone may not enter the aqueous phase efficiently. Even if ozone is destroyed or its production suppressed, photochemical recovery times are on the order of hours, so that tower processing must be centered on a narrow midday time window. The cost of building the number of structures necessary for this brief turnover could be prohibitive. The increase in humidity accompanying mist evaporation could be controlled with condensers, but might otherwise counteract visibility enhancements by recreating aqueous aerosols. Quantification of the divergent forcings convection towers must exert upon the cityscape would call for coupled three dimensional modeling of transport, microphysics, and photochemistry. 112 refs.

This paper examines the properties of a regularization of the Burgers equation in one and multiple dimensions using a filtered convective velocity, which we have dubbed as the convectively filtered Burgers (CFB) equation. A physical motivation behind the filtering technique is presented. An existence and uniqueness theorem for multiple dimensions and a general class of filters is proven. Multiple invariants of motion are found for the CFB equation which are shown to be shared with the viscous and inviscid Burgers equations. Traveling wave solutions are found for a general class of filters and are shown to converge to weak solutions of the inviscid Burgers equation with the correct wave speed. Numerical simulations are conducted in 1D and 2D cases where the shock behavior, shock thickness and kinetic energy decay are examined. Energy spectra are also examined and are shown to be related to the smoothness of the solutions. This approach is presented with the hope of being extended to shock regularization of compressible Euler equations

The effects of magnetic field dependent (MFD) thermosolutal convection and MFD viscosity of the fluid dynamics are investigated between squeezing discs rotating with different velocities. The unsteady constitutive expressions of mass conservation, modified Navier-Stokes, Maxwell and MFD thermosolutal convection are coupled as a system of ordinary differential equations. The corresponding solutions for the transformed radial and azimuthal momentum as well as solutions for the azimuthal and axial induced magnetic field equations are determined, also the MHD pressure and torque which the fluid exerts on the upper disc is derived and discussed in details. In the case of smooth discs the self-similar equations are solved using Homotopy Analysis Method (HAM) with appropriate initial guesses and auxiliary parameters to produce an algorithm with an accelerated and assured convergence. The validity and accuracy of HAM results is proved by comparison of the HAM solutions with numerical solver package BVP4c. It has been shown that magnetic Reynolds number causes to decrease magnetic field distributions, fluid temperature, axial and tangential velocity. Also azimuthal and axial components of magnetic field have opposite behavior with increase in MFD viscosity. Applications of the study include automotive magneto-rheological shock absorbers, novel aircraft landing gear systems, heating up or cooling processes, biological sensor systems and biological prosthetic etc.

Full Text Available A theoretical study of two-dimensional magnetohydrodynamics viscous incompressible free convective boundary layer flow of an electrically conducting, chemically reacting nanofluid from a convectively heated permeable vertical surface is presented. Scaling group of transformations is used in the governing equations and the boundary conditions to determine absolute invariants. A third-order ordinary differential equation which corresponds to momentum conservation and two second-order ordinary differential equations which correspond to energy and nanoparticle volume fraction (species conservation are derived. Our (group analysis indicates that, for the similarity solution, the convective heat transfer coefficient and mass transfer velocity are proportional to x-1/4 whilst the reaction rate is proportional to x-1/2, where x is the axial distance from the leading edge of the plate. The effects of the relevant controlling parameters on the dimensionless velocity, temperature, and nanoparticle volume fraction are examined. The accuracy of the technique we have used was tested by performing comparisons with the results of published work and the results were found to be in good agreement. The present computations indicate that the flow is accelerated and temperature enhanced whereas nanoparticle volume fractions are decreased with increasing order of chemical reaction. Furthermore the flow is strongly decelerated, whereas the nanoparticle volume fraction and temperature are enhanced with increasing magnetic field parameter. Increasing convection-conduction parameter increases velocity and temperatures but has a weak influence on nanoparticle volume fraction distribution. The present study demonstrates the thermal enhancement achieved with nanofluids and also magnetic fields and is of relevance to nanomaterials processing.

Thermal histories have been calculated for simple models of the earth which assume that heat is transported by convection throughout the interior. The application of independent constraints to these solutions limits the acceptable range of the ratio of present radiogenic heat production in the earth to the present surface heat flux. The models use an empirical relation between the rate of convective heat transport and the temperature difference across a convecting fluid. This is combined with an approximate proportionality between effective mantle viscosity and T/sup -n/, where T is temperature and it is argued that n is about 30 throughout the mantle. The large value of n causes T to be strongly buffered against changes in the earth's energy budget and shortens by an order of magnitude the response time of surface heat flux to changes in energy budget as compared to less temperature-dependent heat transport mechanisms. Nevertheless, response times with n=30 are still as long as 1 or 2 b.y. Assuming that the present heat flux is entirely primordial (i.e., nonradiogenic) in a convective model leads back to unrealistically high temperatures about 1.7 b.y. ago. Inclusion of exponentially decaying (i.e., radiogenic) heat sources moves the high temperatures further into the past and leads to a transition from 'hot' to 'cool' calculated thermal histories for the case when the present rate of heat production is near 50% of the present rate of heat loss. Requiring the calculated histories to satisfy minimal geological constraints limits the present heat production/heat loss ratio to between about 0.3 and 0.85. Plausible stronger constraints narrow this range to between 0.45 and 0.65. These results are compatible with estimated radiogentic heat production rates in some meteorites and terrestrial rocks, with a whole-earth K/U ratio of 1--2 x 10 4 giving optimal agreement

Full Text Available In this paper, we re-investigate the problem describing effects of radiation, Joule heating, and viscous dissipation on magnetohydrodynamic Marangoni convection boundary layer over a flat surface with suction/injection. The analytical solution obtained for the reduced system of non-linear-coupled differential equations governing the problem. Laplace transform successfully implemented to get the exact expression for the temperature profile. Furthermore, comparing the current exact results with approximate numerical results obtained using Runge-Kutta-Fehlberg method is introduced. These comparisons declare that the published numerical results agree with the current exact results. In addition, the effects of various parameters on the temperature profile are discussed graphically.

Full Text Available Heat transfer and mass diffusion in nanofluid over a permeable moving surface are investigated. The surface exhibits convective boundary conditions and constant mass diffusion. Effects of Brownian motion and thermophoresis are considered. The resulting partial differential equations are reduced into coupled nonlinear ordinary differential equations using suitable transformations. Shooting technique is implemented for the numerical solution. Velocity, temperature, and concentration profiles are analyzed for different key parameters entering into the problem. Performed comparative study shows an excellent agreement with the previous analysis.

Full Text Available This paper presents the nonsimilarity solutions for mixed convection heat and mass transfer along a semi-infinite vertical plate embedded in a doubly stratified fluid saturated porous medium in the presence of Soret and Dufour effects. The flow in the porous medium is described by employing the Darcy-Forchheimer based model. The nonlinear governing equations and their associated boundary conditions are initially cast into dimensionless forms and then solved numerically. The influence of pertinent parameters on dimensionless velocity, temperature, concentration, heat, and mass transfer in terms of the local Nusselt and Sherwood numbers is discussed and presented graphically.

Full Text Available An exact solution to one-dimensional unsteady natural convection flow past an infinite vertical accelerated plate, immersed in a viscous thermally stratified fluid is investigated. Pressure work term and the vertical temperature advection are considered in the thermodynamic energy equation. The dimensionless governing equations are solved by Laplace Transform techniques for the Prandtl number unity. The velocity and temperature profiles as well as the skin-friction and the rate of heat transfer are presented graphically and discussed the effects of the Grashof number Gr, stratification parameter S at various times t.

The mixed convection boundary layer flow through a stable stratified porous medium bounded by a vertical surface is investigated. The external velocity and the surface temperature are assumed to vary as x m , where x is measured from the leading edge of the vertical surface and m is a constant. Numerical solutions for the governing Darcy and energy equations are obtained. The results indicate that the thermal stratification significantly affects the surface shear stress as well as the surface heat transfer, besides delays the boundary layer separation

Unsteady natural convection of a heat-generating fluid with phase transitions in the enclosures of a square section with isothermal rigid walls is investigated numerically for a wide range of dimensionless parameters. The quasisteady state solutions of conjugate heat and mass transfer problem are compared with available experimental results. Correlation relations for heat flux distributions at the domain boundaries depending on Rayleigh and Ostrogradskii numbers are obtained. It is shown that generally heat transfer is governed both by natural circulation and crust formation phenomena. Results of this paper may be used for analysis of experiments with prototypic core materials.

Full Text Available The paper deals with a degenerate reaction-diffusion equation, including aggregative movements and convective terms. The model also incorporates a real parameter causing the change from a purely diffusive to a diffusive-aggregative and to a purely aggregative regime. Existence and qualitative properties of traveling wave solutions are investigated, and estimates of their threshold speeds are furnished. Further, the continuous dependence of the threshold wave speed and of the wave profiles on a real parameter is studied, both when the process maintains its diffusion-aggregation nature and when it switches from it to another regime.

A simple mathematical theory is proposed for the analysis of natural convective motion, at low Rayleigh number, from a concentrated source of heat in a fluid-saturated porous medium. The theory consists of retaining only the leading terms of series expansions of the dependent variables in terms of the Rayleigh number, is thus linear, and is valid only in the limit of small Rayleigh number. Based on fundamental results for a variety of isolated sources, superposition is used to provide solutions for situations of practical interest. Special emphasis is given to the analysis of sub-seabed disposal of nuclear waste. 8 figures

In this dissertation, we examine several different aspects of computing the numerical solution of the convection-diffusion equation. The solution of this equation often exhibits sharp gradients due to Dirichlet outflow boundaries or discontinuities in boundary conditions. Because of the singular-perturbed nature of the equation, numerical solutions often have severe oscillations when grid sizes are not small enough to resolve sharp gradients. To overcome such difficulties, the streamline diffusion discretization method can be used to obtain an accurate approximate solution in regions where the solution is smooth. To increase accuracy of the solution in the regions containing layers, adaptive mesh refinement and mesh movement based on a posteriori error estimations can be employed. An error-adapted mesh refinement strategy based on a posteriori error estimations is also proposed to resolve layers. For solving the sparse linear systems that arise from discretization, goemetric multigrid (MG) and algebraic multigrid (AMG) are compared. In addition, both methods are also used as preconditioners for Krylov subspace methods. We derive some convergence results for MG with line Gauss-Seidel smoothers and bilinear interpolation. Finally, while considering adaptive mesh refinement as an integral part of the solution process, it is natural to set a stopping tolerance for the iterative linear solvers on each mesh stage so that the difference between the approximate solution obtained from iterative methods and the finite element solution is bounded by an a posteriori error bound. Here, we present two stopping criteria. The first is based on a residual-type a posteriori error estimator developed by Verfurth. The second is based on an a posteriori error estimator, using local solutions, developed by Kay and Silvester. Our numerical results show the refined mesh obtained from the iterative solution which satisfies the second criteria is similar to the refined mesh obtained from

Full Text Available Abstract In this study, we devote ourselves to establishing a stabilized mixed finite element (MFE reduced-order extrapolation (SMFEROE model holding seldom unknowns for the two-dimensional (2D unsteady conduction-convection problem via the proper orthogonal decomposition (POD technique, analyzing the existence and uniqueness and the stability as well as the convergence of the SMFEROE solutions and validating the correctness and dependability of the SMFEROE model by means of numerical simulations.

In this study, we devote ourselves to establishing a stabilized mixed finite element (MFE) reduced-order extrapolation (SMFEROE) model holding seldom unknowns for the two-dimensional (2D) unsteady conduction-convection problem via the proper orthogonal decomposition (POD) technique, analyzing the existence and uniqueness and the stability as well as the convergence of the SMFEROE solutions and validating the correctness and dependability of the SMFEROE model by means of numerical simulations.

Full Text Available The high-resolution analysis and nowcasting system INCA (Integrated Nowcasting through Comprehensive Analysis developed at the Austrian national weather service provides three-dimensional fields of temperature, humidity, and wind on an hourly basis, and two-dimensional fields of precipitation rate in 15 min intervals. The system operates on a horizontal resolution of 1 km and a vertical resolution of 100–200 m. It combines surface station data, remote sensing data (radar, satellite, forecast fields of the numerical weather prediction model ALADIN, and high-resolution topographic data. An important application of the INCA system is nowcasting of convective precipitation. Based on fine-scale temperature, humidity, and wind analyses a number of convective analysis fields are routinely generated. These fields include convective boundary layer (CBL flow convergence and specific humidity, lifted condensation level (LCL, convective available potential energy (CAPE, convective inhibition (CIN, and various convective stability indices. Based on the verification of areal precipitation nowcasts it is shown that the pure translational forecast of convective cells can be improved by using a decision algorithm which is based on a subset of the above fields, combined with satellite products.

Radiation is the dominant mode of heat transfer in large fires. However, convection can be as much as 10 to 20 percent of the total heat transfer to an object in a large fire. The current radioactive material transportation packaging regulations include convection as a mode of heat transfer in the accident condition scenario. The current International Atomic Energy Agency Safety Series 6 packaging regulation states ''the convection coefficient shall be that value which the designer can justify if the package were exposed to the specified fire''. The current Title 10, Code of Federal Regulations, Part 71 (10CFR71) packaging regulation states ''when significant, convection heat input must be included on the basis of still, ambient air at 800 degrees C (1475 degrees F)''. Two questions that can arise in an analysts mind from an examination of the packaging regulations is whether convection is significant and whether convection should be included in the design analysis of a radioactive materials transportation container. The objective of this study is to examine the convective effects on an actual radioactive materials transportation package using a regulatory and a proposed thermal boundary condition

An answer is suggested to the question of why plasma and magnetic energy accumulate in the Earth's magnetotail to be released in sporadic events, namely substorms. It is shown that the idea of steady convection is inconsistent with the idea of slow, approximately lossless, plasma convection in a long, closed-field-line region that extends into a long magnetotail, such as occurs during Earthward convection in the Earth's plasma sheet. This inconsistency is argued generally and demonstrated specifically using several quantitative models of the Earth's magnetospheric magnetic field. These results suggest that plasma-sheet convection is necessarily time dependent. If flux tubes are to convect adiabatically earthward, the confining magnetic pressure in the tail lobes must increase with time, and the magnetotail must evolve into a more stretched configuration. Eventually, the magnetosphere must find some way to release plasma from inner-plasma-sheet flux tubes. This suggests an obvious role for the magnetospheric substorm in the convection process. To probe this process further, a two-dimensional, self-consistent, quasi-static convection model was developed. This model self consistently includes a dipole field and can reasonably account for the effects of inner-magnetospheric shielding

The discovery of three Super-Earths around different stars, possible only in the last year, prompts us to study the characteristics of our planet within a general context. The Earth, being the most massive terrestrial object in the solar system is the only planet that exhibits plate tectonics. We think this might not be a coincidence and explore the role that mass plays in determining the mode of convection. We use the scaling of convective vigor with Rayleigh number commonly used in parameterized convection. We study how the parameters controlling convection: Rayleigh number (Ra), boundary layer thickness (δ), internal temperature (T_i) and convective velocities (u) scale with mass. This is possible from the scaling of heat flux, mantle density, size and gravity with mass which we reported in Valencia, et. al 2006. The extrapolation to massive rocky planets is done from our knowledge of the Earth. Even though uncertainties arise from extrapolation and assumptions are needed we consider this simple scaling to be a first adequate step. As the mass of a planet increases, Ra increases, yielding a decrease in δ and an increase in u, while T_i increases very slightly. This is true for an isoviscous case and is more accentuated in a temperature dependent viscosity scenario. In a planet with vigorous convection (high u), a thin lithosphere (low δ) is easier to subduct and hence, initiate plate tectonics. The lithosphere also has to be dense enough (cold and thick) to have the bouyancy necessary for subduction. We calculate that a convective cycle for an isoviscous planet is τ ~ M^{-0.3} considering whole mantle convection. Meaning that if these planets have continents, the timescale for continental rearrangement is shorter (about half the Earth's for a 5 earth-mass planet). Additionally, we explore the negative feedback cycle between convection and temperature dependent viscosity and estimate a timescale for this effect.

The conjugate heat transfer (CHT) problem takes into account the thermal interaction between a body and fluid flowing over or through it, a key consideration in both mechanical and aerospace engineering. Presenting more than 100 solutions of non-isothermal and CHT problems, this title considers the approximate solutions of CHT problems.

In certain boundary layer or natural convection work, where a similarity transformation is valid, the equations can be reduced to a set of nonlinear ordinary differential equations. They are therefore well-suited to a fast solution on an analog/hybrid computer. This paper illustrates such usage of the analog/hybrid computer by a set of…

Cell survival upon cryopreservation is affected by the cooling rate. However, it is difficult to model the heat transfer process or to predict the cooling curve of a cryoprotective agent (CPA) solution due to the uncertainty of its convective heat transfer coefficient (h). To measure the h and to better understand the heat transfer process of cryovials filled with CPA solution being plunged in liquid nitrogen. The temperatures at three locations of the CPA solution in a cryovial were measured. Different h values were selected after the cooling process was modeled as natural convection heat transfer, the film boiling and the nucleate boiling, respectively. And the temperatures of the selected points are simulated based on the selected h values. h was determined when the simulated temperature best fitted the experimental temperature. When the experimental results were best fitted, according to natural convection heat transfer model, h(1) = 120 W/(m(2)·K) while due to film boiling and nucleate boiling regimes h(f) = 5 W/(m(2)·K) followed by h(n) = 245 W/(m(2)·K). These values were verified by the differential cooling rates at the three locations of a cryovial. The heat transfer process during cooling in liquid nitrogen is better modeled as film boiling followed by nucleate boiling.

Discoloration and browning are caused primarily by various reactions, including Maillard condensation of hexoses and amino components, phenol polymerization and pigment destruction. Convective drying can be combined with various pretreatments to help reduce undesired color changes and improve color parameters of dried products. In this study, effects of ultrasound-assisted osmotic dehydration as a pretreatment before convective drying on color parameters of Mirabelle plum were investigated. Variations of L* (lightness), a* (redness/greenness), b* (yellowness/blueness), total color change (ΔE), chroma, hue angle and browning index values were presented versus drying time during convective drying of control and pretreated Mirabelle plums as influenced by ultrasonication time, osmotic solution concentration and immersion time in osmotic solution. Samples pretreated with ultrasound for 30 min and osmotic solution concentration of 70% had a more desirable color among all other pretreated samples, with the closest L*, a* and b* values to the fresh one, showing that ultrasound and osmotic dehydration are beneficial to the color of final products after drying.

A critical challenge for assessing regional climate change projections relies on improving the estimate of atmospheric aerosol impact on clouds and reducing the uncertainty associated with the use of parameterizations. In this sense, the horizontal grid spacing implemented in state-of-the-art regional climate simulations is typically 10-25 kilometers, meaning that very important processes such as convective precipitation are smaller than a grid box, and therefore need to be parameterized. This causes large uncertainties, as closure assumptions and a number of parameters have to be established by model tuning. Convection is a physical process that may be strongly conditioned by atmospheric aerosols, although the solution of aerosol-cloud interactions in warm convective clouds remains nowadays a very important scientific challenge, rendering parametrization of these complex processes an important bottleneck that is responsible from a great part of the uncertainty in current climate change projections. Therefore, the explicit simulation of convective processes might improve the quality and reliability of the simulations of the aerosol-cloud interactions in a wide range of atmospheric phenomena. Particularly over the Mediterranean, the role of aerosol particles is very important, being this a crossroad that fuels the mixing of particles from different sources (sea-salt, biomass burning, anthropogenic, Saharan dust, etc). Still, the role of aerosols in extreme events in this area such as medicanes has been barely addressed. This work aims at assessing the role of aerosol-atmosphere interaction in medicanes with the help of the regional chemistry/climate on-line coupled model WRF-CHEM run at a convection-permitting resolution. The analysis is exemplary based on the "Rolf" medicane (6-8 November 2011). Using this case study as reference, four sets of simulations are run with two spatial resolutions: one at a convection-permitting configuration of 4 km, and other at the

In this study, we conduct a two-dimensional numerical analysis of double diffusive natural convection in an emplacement drift for a nuclear waste repository. In-drift heat and moisture transport is driven by combined thermal- and compositional-induced buoyancy forces. Numerical results demonstrate buoyancy-driven convective flow patterns and configurations during both repository heat-up and cool-down phases. It is also shown that boundary conditions, particularly on the drip-shield surface, have strong impacts on the in-drift convective flow and transport

A critical physical model, based on the ion temperature gradient (ITG) mode and the trapped electron mode (TEM), trying to explain the spatio-temporal dynamics of anomalous particle convection reversal (i.e., the particle convective flux reverses from inward to outward), is developed numerically. The dependence of density peaking and profile shape on the particle convection is studied. Only the inward pinch could lead to the increase of the density peaking. The validation of the critical model is also analyzed. A comparison of the estimates calculated by the model and the experimental results from the Tore Supra tokamak shows that they are qualitatively both consistent. (paper)

This book is one of the first devoted to an account of theories of thermal convection which involve local thermal non-equilibrium effects, including a concentration on microfluidic effects. The text introduces convection with local thermal non-equilibrium effects in extraordinary detail, making it easy for readers newer to the subject area to understand. This book is unique in the fact that it addresses a large number of convection theories and provides many new results which are not available elsewhere. This book will be useful to researchers from engineering, fluid mechanics, and applied mathematics, particularly those interested in microfluidics and porous media.

In this work the nature of confinement improvement implied by the self-consistent generation of mean flows in two-dimensional convective turbulence is studied. The confinement variations are linked to two distinct regulation mechanisms which are also shown to be at the origin of low......-frequency bursting in the fluctuation level and the convective heat flux integral, both resulting in a state of large-scale intermittency. The first one involves the control of convective transport by sheared mean flows. This regulation relies on the conservative transfer of kinetic energy from tilted fluctuations...

Interim storage technology for spent fuel by dry storage casks have been investigated. The casks are vertically placed in a storage building. The decay heat is removed from the outer cask surface by natural convection of air entering from the building wall to the roof. The air flow pattern in the storage building was governed by the natural driving pressure difference and circulating flow. The purpose of this study is to understand the mechanism of the removal of decay heat from casks by natural convection. The simulated flow conditions in the building were assumed as a natural and forced combined convection and were investigated by the turbulent quantities near wall. (author)

Wastewater contaminated by heavy metals pose great challenges as they are non biodegradable, toxic and carcinogenic to the soil and aquifers. Vermiculite blended with chitosan have been used to remove Cr(VI) and Cd(II) from the industrial wastewater. The results indicate that the vermiculite blended with chitosan adsorb Cr(VI) and Cd(II) from industrial waste water. Batch adsorption experiments were performed as a function of pH 5.0 and 5.5 respectively for chromium and cadmium. The adsorption rate was observed to be 72 and 71 % of chromium and cadmium respectively. The initial optimum contact time for Cr(VI) was 300 min with 59.2 % adsorption and 300 min for Cd(II) with 71.5 % adsorption. Whereas, at 4-6 there is saturation, increasing the solid to liquid ratio for chitosan biopolymers increases the number of active sites available for adsorption. The optimum pH required for maximum adsorption was found to be 5.0 and 5.5 for chromium and cadmium respectively. The experimental equilibrium adsorption data were fitted using Langmuir and Freundlich equations. It was observed that adsorption kinetics of both the metal ions on vermiculite blended chitosan is well be analyzed with pseudo-second-order model. The negative free energy change of adsorption indicates that the process was spontaneous and vermiculite blended chitosan was a favourable adsorbent for both the metals.

Under an arbitrary time-dependent heating of an infinite vertical plate (or wall), the steady viscosity-dependent free convection flow of a viscous incompressible fluid is investigated. Using the asymptotic method of solution on the governing equations of motion and energy, the resulting Ordinary differential equations were ...

Climate models are known to have difficulty in simulating tropical diurnal convections that exhibit distinct characteristics over land and open ocean. While the causes are rooted in deficiencies in convective parameterization in general, lack of representations of mesoscale dynamics in terms of land-sea breeze, convective organization, and propagation of convection-induced gravity waves also play critical roles. In this study, the problem is investigated at the process-level with the U.S. Department of Energy Accelerated Climate Modeling for Energy (ACME) model in short-term hindcast mode using the Cloud Associated Parameterization Testbed (CAPT) framework. Convective-scale radar retrievals and observation-driven convection-permitting simulations for the Tropical Warm Pool-International Cloud Experiment (TWP-ICE) cases are used to guide the analysis of the underlying processes. The emphasis will be on linking deficiencies in representation of detailed process elements to the model biases in diurnal convective properties and their contrast among inland, coastal and open ocean conditions.

A two-dimensional axisymmetric swirling model based on the lattice Boltzmann method (LBM) in a pseudo Cartesian coordinate system is posited to simulate Czochralski (Cz) crystal growth in this paper. Specifically, the multiple-relaxation-time LBM (MRT-LBM) combined with the finite difference method (FDM) is used to analyze the melt convection and heat transfer in the process of Cz crystal growth. An incompressible axisymmetric swirling MRT-LB D2Q9 model is applied to solve for the axial and radial velocities by inserting thermal buoyancy and rotational inertial force into the two-dimensional lattice Boltzmann equation. In addition, the melt temperature and the azimuthal velocity are solved by MRT-LB D2Q5 models, and the crystal temperature is solved by FDM. The comparison results of stream functions values of different methods demonstrate that our hybrid model can be used to simulate the fluid-thermal coupling in the axisymmetric swirling model correctly and effectively. Furthermore, numerical simulations of melt convection and heat transfer are conducted under the conditions of high Grashof (Gr) numbers, within the range of 105 ˜ 107, and different high Reynolds (Re) numbers. The experimental results show our hybrid model can obtain the exact solution of complex crystal-growth models and analyze the fluid-thermal coupling effectively under the combined action of natural convection and forced convection.

Views of the northern hemisphere auroral distribution obtained by the Viking satellite present a qualitative means of inferring the convective patterns which occur during interplanetary magnetic field (IMF) B z northward. The approach is taken whereby upward field-aligned currents are assumed to be coincident with large-scale discrete auroral features and on this basis possible convective patterns are deduced. While the patterns are not unique solutions, they are found to be consistent with merging theory predictions. That is, for B z northward the auroral observations support the possibility of three and/or four cell patterns. When the IMF azimuthal angle is 90 degree (270 degree), a clockwise (anticlockwise) cell is found to be located in the polar region between the two standard viscous cells. When IMF B x dominates and is in a toward orientation, convection stagnates, whereas if B x is negative, a four-cell pattern may form with sunward flow at very high latitudes. The concept of using global auroral images as an additional tool when developing convection models could prove to be necessary in order to extend beyond the few isolated measurements taken in situ by satellites

Over the past 15 yr, numerical models of convection in Earth's mantle have made a leap forward: they can now produce self-consistent plate-like behaviour at the surface together with deep mantle circulation. These digital tools provide a new window into the intimate connections between plate tectonics and mantle dynamics, and can therefore be used for tectonic predictions, in principle. This contribution explores this assumption. First, initial conditions at 30, 20, 10 and 0 Ma are generated by driving a convective flow with imposed plate velocities at the surface. We then compute instantaneous mantle flows in response to the guessed temperature fields without imposing any boundary conditions. Plate boundaries self-consistently emerge at correct locations with respect to reconstructions, except for small plates close to subduction zones. As already observed for other types of instantaneous flow calculations, the structure of the top boundary layer and upper-mantle slab is the dominant character that leads to accurate predictions of surface velocities. Perturbations of the rheological parameters have little impact on the resulting surface velocities. We then compute fully dynamic model evolution from 30 and 10 to 0 Ma, without imposing plate boundaries or plate velocities. Contrary to instantaneous calculations, errors in kinematic predictions are substantial, although the plate layout and kinematics in several areas remain consistent with the expectations for the Earth. For these calculations, varying the rheological parameters makes a difference for plate boundary evolution. Also, identified errors in initial conditions contribute to first-order kinematic errors. This experiment shows that the tectonic predictions of dynamic models over 10 My are highly sensitive to uncertainties of rheological parameters and initial temperature field in comparison to instantaneous flow calculations. Indeed, the initial conditions and the rheological parameters can be good enough

Full Text Available `The aim of this analysis is to investigate the existence of the dual solutions for magnetohydrodynamic (MHD flow of an upper-convected Maxwell (UCM fluid over a porous shrinking wall. We have employed the Lie group analysis for the simplification of the nonlinear differential system and computed the absolute invariants explicitly. An efficient numerical technique namely the shooting method has been employed for the constructions of solutions. Dual solutions are computed for velocity profile of an upper-convected Maxwell (UCM fluid flow. Plots reflecting the impact of dual solutions for the variations of Deborah number, Hartman number, wall mass transfer are presented and analyzed. Streamlines are also plotted for the wall mass transfer effects when suction and blowing situations are considered.

Large-scale electric fields associated with storms or substorms are responsible for inward convection and energization of plasma sheet plasma. Calculations based on steady state convection theory show that the response to such electric fields qualitatively accounts for many features of the injected particle distribution, but quantitative agreement with the theory has not yet been obtained. It is known that the predictions can be improved by introducing the concept of convection in response to a time dependent electric field. On the other hand, time dependent calculations are sensitive to the choice of initial conditions, and most models have failed to incorporate these conditions in a realistic and self-consistent manner. In this paper we present a more complete model consisting of realisic initial conditions and time dependent convection to explain a typical substorm-associated electron injection event. We find very good agreement between the observed electron flux changes and those predicted by our model

We analyse the boundary layer (BL) equations in natural thermal convection, which includes vertical convection (VC), where the fluid is confined between two differently heated vertical walls, horizontal convection (HC), where the fluid is heated at one part of the bottom plate and cooled at some other part, and Rayleigh-Benard convection (RBC). For BL dominated regimes we derive the scaling relations of the Nusselt and Reynolds numbers (Nu, Re) with the Rayleigh and Prandtl numbers (Ra, Pr). For VC the scaling relations are obtained directly from the BL equations, while for HC they are derived by applying the Grossmann-Lohse theory to the case of VC. In particular, for RBC with large Pr we derive Nu Pr0Ra1/3 and Re Pr-1Ra2/3. The work is supported by the Deutsche Forschungsgemeinschaft (DFG) under the Grant Sh 405/4 - Heisenberg fellowship.

We examine how metallicity affects convection and overshoot in the superadiabatic layer of main sequence stars. We present results from a grid of three-dimensional radiation hydrodynamic simulations with four metallicities (Z = 0.040, 0.020, 0.010, 0.001), and spanning a range in effective temperature (4950 eff < 6230). We show that changing the metallicity alters properties of the convective gas dynamics, and the structure of the superadiabatic layer and atmosphere. Our grid of simulations shows that the amount of superadiabaticity, which tracks the transition from efficient to inefficient convection, is sensitive to changes in metallicity. We find that increasing the metallicity forces the location of the transition region to lower densities and pressures, and results in larger mean and turbulent velocities throughout the superadiabatic region. We also quantify the degree of convective overshoot in the atmosphere, and show that it increases with metallicity as well.

We present the first three-dimensional simulations of fingering convection performed at parameter values approaching those relevant for astrophysics. Our simulations reveal the existence of simple asymptotic scaling laws for turbulent heat and compositional transport, which can be straightforwardly extrapolated from our numerically tractable values to the true astrophysical regime. Our investigation also indicates that thermo-compositional 'staircases', a key consequence of fingering convection in the ocean, cannot form spontaneously in the fingering regime in stellar interiors. Our proposed empirically determined transport laws thus provide simple prescriptions for mixing by fingering convection in a variety of astrophysical situations, and should, from here on, be used preferentially over older and less accurate parameterizations. They also establish that fingering convection does not provide sufficient extra-mixing to explain observed chemical abundances in red giant branch stars.

Unusual convective behaviour can occur in mixtures of gases and heavy vapour, including stabilization of mixtures hot at the base and 'upside-down' convection in mixtures hot at the top. Previous work produced a criterion for this behaviour which ignored the necessary presence of an aerosol. Modification arising from aerosol condensation is derived and is shown to involve the Lewis and condensation numbers of the mixture, as well as a quantity involving the temperature drop across a boundary layer. It becomes negligible at high temperatures, but can crucially affect the temperature for the onset of unusual behaviour. Aerosol formation produces an asymmetry between the convective forces in boundary layers in which the mixture is being heated and cooled, respectively, for example at the base and roof of a cavity. The convective behaviour discussed could occur in situations relevant to nuclear safety. (author)

radiation effects on mixed convection heat and mass transfer over a vertical plate in ... numerically by finite difference method and analytically by perturbation. ... Brinkman equation was used to model the flow in the porous region. The.

Oct 1, 2013 ... tical cylinder with combined effects of heat and mass transfer is an ... presented a numerical study of free convective flow of a viscous ... models. The simultaneous effects of thermal and mass stratifications have application.

The magnetic fields of Earth and other planets are generated by turbulent, rotating convection in liquid metal. Liquid metals are peculiar in that they diffuse heat more readily than momentum, quantified by their small Prandtl numbers, Pr rotating Rayleigh-Bénard convection experiments in the liquid metal gallium (Pr = 0.025) over a range of nondimensional buoyancy forcing (Ra) and rotation periods (E). Our primary diagnostic is the efficiency of convective heat transfer (Nu). In general, we find that the convective behavior of liquid metal differs substantially from that of moderate Pr fluids, such as water. In particular, a transition between rotationally constrained and weakly rotating turbulent states is identified, and this transition differs substantially from that observed in moderate Pr fluids. This difference, we hypothesize, may explain the different classes of magnetic fields observed on the Gas and Ice Giant planets, whose dynamo regions consist of Pr 1 fluids, respectively.

Organized convection in the tropics occurs across a range of spatial and temporal scales and strongly influences cloud cover and humidity. One mode of organization found is ``self-aggregation,'' in which moist convection spontaneously organizes into one or several isolated clusters despite spatially homogeneous boundary conditions and forcing. Self-aggregation is driven by interactions between clouds, moisture, radiation, surface fluxes, and circulation, and occurs in a wide variety of idealized simulations of radiative-convective equilibrium. Here we provide a review of convective self-aggregation in numerical simulations, including its character, causes, and effects. We describe the evolution of self-aggregation including its time and length scales and the physical mechanisms leading to its triggering and maintenance, and we also discuss possible links to climate and climate change.

The structure of mantle convection will greatly influence the generation and the survival of compositional heterogeneities. Conversely, geochemical observations can be used to obtain information about heterogeneities in the mantle and then, with certain model assumptions, information about the